List of uniform Euclidean honeycombs

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Even excluding infinite families, the complete set of uniform honeycombs of 3D Euclidean space is unknown. 41 of them are convex.

Category A: Polygon-apeirogon duoprisms[edit | edit source]

This is the infinite set of duoprisms between an apeirogon and any other regular polygon. Each of them looks like a column of n-gonal prisms, with apeirogonal prisms on the sides.

Category B: Subdivisions[edit | edit source]

These are the honeycombs with multiple apeiratic cells in the same plane. Their vertex figures have coplanar faces. For each honeycomb in this category, there is an analogous honeycomb somewhere else where each stack of apeiratic cells is replaced by a single apeiratic cell.

Category 1: Primaries[edit | edit source]

The two members of the chon regiment with full (o4o3o4x) or half (o3o4x *b3o) symmetry, as well as the fully symmetric members of the octet regiment.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
1 Cubic honeycomb Chon x4o3o4o () Octahedron Cubes Chon P4
2 Cubihemisquare honeycomb Cuhsquah /2 Tetrahemihexahedron Cubes
Square tilings
Chon S4
3 Tetrahedral-octahedral honeycomb Octet Cuboctahedron Tetrahedra
Octahedra
Octet S4
4 Tetrahemitriangular honeycomb Tehtrah Octahemioctahedron Tetrahedra
Triangular tilings
Octet S4
5 Octahemitriangular honeycomb Ohtrah () /2 Cubohemioctahedron Octahedra
Triangular tilings
Octet S4
6 Octahedral-tomotetrahedral honeycomb Octutoh Octahedra
Truncated tetrahedra
Octet S4
7 Tomotetrahedral-hemitriangular honeycomb Tuthtrah Triangular tilings
Truncated tetrahedra
Octet S4
8 Cuboctahedral-hemitriangular honeycomb Cohtrah Triangular tilings
Cuboctahedra
Octet S4
9 Tetrahedral-cuboctahedral honeycomb Tetcoh o4x3o4o *aØo3*c Tetrahedra
Cuboctahedra
Octet S4
10 Tomotetrahedral-cuboctahedral honeycomb Tutcoh Truncated tetrahedra
Cuboctahedra
Octet S4
11 Octahedral-octahemioctahedral-hemihexagonal honeycomb Ohohaht Octahedra
Octahemioctahedra
Hexagonal tilings
Octet S4
12 Tetrahedral-octahemioctahedral-hemihexagonal honeycomb Tohohaht Tetrahedra
Octahemioctahedra
Hexagonal tilings
Octet S4
13 Cubohemioctahedral-hemihexagonal honeycomb Chohaht Cubohemioctahedra
Hexagonal tilings
Octet S4

Category 2: Truncates[edit | edit source]

These are the truncates of the honeycombs from category 1 that have uniform vertex figures.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
14 Truncated cubic honeycomb Tich x4x3o4o () Square pyramid Truncated cubes
Octahedra
Tich R4
15 Truncated cubihemisquare honeycomb Ticuhsquah () /2 Bowtie pyramid Truncated cubes
Truncated square tilings
Tetrahemihexahedra
Tich S4
16 Truncated tetrahedral-octahedral honeycomb Tatoh Rectangular pyramid Truncated tetrahedra
Truncated octahedra
Cuboctahedra
Tatoh S4
17 Truncated tetrahedral-hemitriangular honeycomb Tutehtrah Bowtie pyramid Octahemioctahedra
Truncated tetrahedra
Hexagonal tilings
Tatoh S4
18 Truncated octahedral-hemitriangular honeycomb Tohtrah ()/2 Bowtie pyramid Cubohemioctahedra
Truncated octahedra
Hexagonal tilings
Tatoh S4
19 Quasitruncated cubic honeycomb Quitch x4/3x3o4o () Square pyramid Quasitruncated hexahedra
Octahedra
Quitch R4
20 Quasitruncated cubihemisquare honeycomb Quitcuhsquah (x3o3/2x4/3x4/3*a)/2 Bowtie pyramid Quasitruncated hexahedra
Quasitruncated square tilings
Tetrahemihexahedra
Quitch S4
21 Bitruncated cubic honeycomb Batch o4x3x4o () Tetragonal disphenoid Truncated octahedra Batch R4×2

Category 3: Rich Regiment[edit | edit source]

Rich is the rectified cubic honeycomb. Its regiment contains 49 members, whose vertex figures are facetings of square prisms.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
22 Rectified cubic honeycomb Rich o4x3o4o () Square prism Octahedra
Cuboctahedra
Rich R4
23 Disoctahemiapeiratic honeycomb Doha Square hourglass Octahedra
Triangular-hemiapeirogonal tilings
Rich R4
24 Cuboctahedral hemiapeiratic honeycomb Coha Cuboctahedra
Triangular-hemiapeirogonal tilings
Rich R4
25 Hemioctahedral hemiapeiratic honeycomb Hohah Cubohemioctahedra
Hexagonal-hemiapeirogonal tilings
Rich R4
26 Octahedral hemioctahedral hemiapeiratic honeycomb Ohoha Octahedra
Octahemioctahedra
Hexagonal-hemiapeirogonal tilings
Rich R4
27 Octahedral hemioctahedral hemitrihexagonal honeycomb Ohohath Octahedra
Cubohemioctahedra
Trihexagonal tilings
Rich R4
28 Hemioctahedral hemitrihexagonal honeycomb Hohath Octahemioctahedra
Trihexagonal tilings
Rich R4
29 Cubatidishemiapeiratic honeycomb Cuhada (x3o3/2x4/3o4*a~*c)/2 Cuboctahedra
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
30 Octahedral hemioctahedral dishemiapeiratic honeycomb Ocodaha Octahedra
Cuboctahedra
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
31 Hemihexahedral hemioctahedral dishemiapeiratic honeycomb Hahodaha Tetrahemihexahedra
Octahemioctahedra
Square-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
32 Hemihexahedral cuboctahedral hemioctahedral dishemiapeiratic honeycomb Hahcohodaha Tetrahemihexahedra
Cuboctahedra
Cubohemioctahedra
Square-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
33 Hemihexahedral cuboctahedral hemioctahedral hemitrihexagonal hemisquare honeycomb Hahcohohathash Tetrahemihexahedra
Cuboctahedra
Octahemioctahedra
Trihexagonal tilings
Square tilings
Rich S4
34 Hemihexahedral hemioctahedral hemitrihexagonal hemisquare honeycomb Hahohathash Tetrahemihexahedra
Cubohemioctahedra
Trihexagonal tilings
Square tilings
Rich S4
35 Hemihexahedral dishemioctahedral hemitrihexagonal hemisquare honeycomb Hahdhodahthash Tetrahemihexahedra
Octahemioctahedra
Cubohemioctahedra
Trihexagonal tilings (two types)
Square tilings
Rich S4
36 Rectified cubihemisquare honeycomb Ricuhsquah () /2 Tetrahemihexahedra
Cuboctahedra
Square tilings
Rich S4
37 Rectified tetrahemitriangular honeycomb Retehtrah Octahedra
Octahemioctahedra
Trihexagonal tilings
Rich S4
38 Rectified octahemitriangular honeycomb Rohtrah () /2 Cuboctahedra
Cubohemioctahedra
Trihexagonal tilings
Rich S4
39 Hemihexahedral dishemiapeiratic honeycomb Hahdha Tetrahemihexahedra
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
40 Octahemioctahedral dishemiapeiratic honeycomb Ohodaha Octahemioctahedra
Triangular-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
41 Cubohemioctahedral dishemiapeiratic honeycomb Chodaha Cubohemioctahedra
Square-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
42 Hemihexahedral discuboctahedral dishemiapeiratic honeycomb Hahdcodaha Tetrahemihexahedra
Cuboctahedra (two types)
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
43 Octahedral hemioctahedral cuboctahedral dishemiapeiratic honeycomb Ohocodaha Octahedra
Cuboctahedra
Octahemioctahedra
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
44 Octahedral cuboctahedral hemioctahedral dishemiapeiratic honeycomb Ocohodaha Octahedra
Cuboctahedra
Cubohemioctahedra
Triangular-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
45 Hemihexahedral dishemioctahedral hemitrihexagonal dishemiapeiratic honeycomb Hahdhohathadha Tetrahemihexahedra
Cubohemioctahedra (two types)
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Trihexagonal tilings
Rich S4
46 Hemihexahedral dishemioctahedral hemisquare dishemiapeiratic honeycomb Hahdhohashadha Tetrahemihexahedra
Octahemioctahedra
Cubohemioctahedra
Hexagonal-hemiapeirogonal tilings
Triangular-hemiapeirogonal tilings
Square tilings
Rich S4
47 Hemihexahedral hemioctahedral hemioctahedral hemitrihexagonal dishemiapeiratic honeycomb Hahohohathadha Tetrahemihexahedra
Octahemioctahedra (two types)
Square-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Trihexagonal tilings
Rich S4
48 Dishemioctahedral hemitrihexagonal dishemiapeiratic honeycomb Dahohathadha Octahemioctahedra
Cubohemioctahedra
Trihexagonal tilings
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
49 Hemihexahedral hemioctahedral hemisquare dishemiapeiratic honeycomb Hahohashadha Tetrahemihexahedra
Cubohemioctahedra
Square tilings
Triangular-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich S4
50 Hemihexahedral hemioctahedral hemitrihexagonal dishemiapeiratic honeycomb Hahohathadha Tetrahemihexahedra
Octahemioctahedra
Trihexagonal tilings
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
51 Cuboctahedral hemioctahedral hemitrihexagonal hemidiapeiratic honeycomb Cohohathadha Cuboctahedra
Octahemioctahedra
Trihexagonal tilings
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
52 Octahedral hemioctahedral hemitrihexagonal hemidiapeiratic honeycomb Ohohathadha Octahedra
Cubohemioctahedra
Trihexagonal tilings
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich S4
53 Hemihexahedral cuboctahedral hemisquare hemidiapeiratic honeycomb Hahcohashadha Tetrahemihexahedra
Cuboctahedra
Triangular-hemiapeirogonal tilings (two types)
Square tilings
Rich S4
54 Hemioctahedral tomooctahedral honeycomb Hotoh Cubohemioctahedra
Truncated octahedra
Rich S4
55 Tomooctahedral hemiapeiratic honeycomb Toha Truncated octahedra
Hexagonal-hemiapeirogonal tilings
Rich S4
56 Hemioctahedral tomooctahedral hemiapeiratic honeycomb Hotoha Octahemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Rich S4
57 Cuboctahedral tomooctahedral hemitrihexagonal honeycomb Cotohath Cuboctahedra
Truncated octahedra
Trihexagonal tilings
Rich S4
58 Octahedral tomooctahedral hemitrihexagonal honeycomb Otohath Octahedra (two types)
Truncated octahedra
Trihexagonal tilings
Rich S4
59 Octahedral hemioctahedral tomooctahedral honeycomb Ohotoh Octahedra (two types)
Octahemioctahedra
Truncated octahedra
Rich S4
60 Tomooctahedral hemioctahedral hemitrihexagonal honeycomb Tohohath Octahemioctahedra
Truncated octahedra
Triangular tilings
Rich P4
61 Disoctahedral cuboctahedral hemioctahedral tomooctahedral hemitrihexagonal honeycomb Docohotohath Octahedra (two types)
Cuboctahedra
Cubohemioctahedra
Truncated octahedra
Trihexagonal tilings
Rich P4
62 Disoctahedral hemioctahedral tomooctahedral disapeiratic honeycomb Dohotoda Octahedra (two types)
Octahemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich P4
63 Cuboctahedral hemioctahedral tomooctahedral disapeiratic honeycomb Cohotoda Cuboctahedra
Cubohemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich P4
64 Tomooctahedral hemioctahedral disapeiratic honeycomb Tohoda Cubohemioctahedra
Truncated octahedra
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich P4
65 Dishemioctahedral tomooctahedral disapeiratic honeycomb Dahotoda Octahemioctahedra
Cubohemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich P4
66 Cuboctahedral tomooctahedral hemitrihexagonal dishemiapeiratic honeycomb Cotohathadha Cuboctahedra
Truncated octahedra
Trihexagonal tilings
Square-hemiapeirogonal tilings
Hexagonal-hemiapeirogonal tilings
Rich P4
67 Disoctahedral cuboctahedral hemioctahedral tomooctahedral dishemiapeiratic honeycomb Docohotodaha Octahedra (two types)
Cuboctahedra
Octahemioctahedra
Truncated octahedra
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich P4
68 Disoctahedral cuboctahedral tomooctahedral hemitrihexagonal dishemiapeiratic honeycomb Docotohathadha Octahedra (two types)
Cuboctahedra
Truncated octahedra
Trihexagonal tilings
Hexagonal-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich P4
69 Disoctahedral dishemioctahedral tomooctahedral dishemiapeiratic honeycomb Dodhotodaha Octahedra (two types)
Octahemioctahedra
Cubohemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Square-hemiapeirogonal tilings
Rich P4
70 Disoctahedral hemioctahedral tomooctahedral hemitrihexagonal dishemiapeiratic honeycomb Dohotohathadha Octahedra (two types)
Cubohemioctahedra
Truncated octahedra
Triangular-hemiapeirogonal tilings
Trihexagonal tilings
Square-hemiapeirogonal tilings
Rich P4

Category 4: Sphenoverts[edit | edit source]

These are the honeycombs with wedge-shaped vertex figures and their regiments.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
71 Small rhombated cubic honeycomb Srich o4x3o4x () Rectangular wedge Small rhombicuboctahedra
Cubes
Cuboctahedra
Srich R4
72 Retrosphenoverted cubaticubatiapeiratic honeycomb Rawvicoca Small cubicuboctahedra
Cubes
Truncated square tilings
Srich R4
73 Small rhombic cubatiapeiratic honeycomb Sirca Small rhombihexahedra
Cubes
Truncated square tilings
Srich R4
74 Small pseudorhombic cubatiapeiratic honeycomb Spiraca Cubes
Truncated square tilings
Great rhombicuboctahedra
Srich R4
75 Grand rhombic dicubatic honeycomb Gardoch Small rhombihexahedra
Great rhombicuboctahedra
Srich R4
76 Cubatiapeirointercepted dicubatic honeycomb Candoch Small rhombicuboctahedra
Cuboctahedra
Truncated square tilings
Great rhombicuboctahedra
Srich R4
77 Cubatiintercepted prismatodicubatic honeycomb Canpadoch Small cubicuboctahedra
Cuboctahedra
Cubes
Great rhombicuboctahedra
Srich R4
78 Sphenoverted cubaticubatiapeiratic honeycomb Wavicoca o4x3o4x4/3*b Great cubicuboctahedra
Cuboctahedra
Quasitruncated square tilings
Wavicoca R4
79 Quasirhombated cubic honeycomb Querch o4x3o4/3x () Quasirhombicuboctahedra
Cubes
Cuboctahedra
Wavicoca R4
80 Great rhombic cubatiapeiratic honeycomb Girca Great rhombihexahedra
Cubes
Quasitruncated square tilings
Wavicoca R4
81 Great pseudorhombic cubatiapeiratic honeycomb Gipraca Cubes
Quasitruncated square tilings
Quasitruncated cuboctahedra
Wavicoca R4
82 Grand quasirhombic dicubatic honeycomb Gaqradoch Great rhombihexahedra
Quasitruncated cuboctahedra
Wavicoca R4
83 Prismatocubatiintercepted dicubatic honeycomb Pacnadoch Great cubicuboctahedra
Cuboctahedra
Cubes
Quasitruncated cuboctahedra
Wavicoca R4
84 Cubatiintercepted dicubatiapeiratic honeycomb Candaca Quasirhombicuboctahedra
Cuboctahedra
Quasitruncated square tilings
Quasitruncated cuboctahedra
Wavicoca R4
85 Sphenoverted cubatiapeiraticubatic honeycomb Wavicac Rectangular wedge Small squarisquariapeirogonal tilings
Quasitruncated hexahedra
Cuboctahedra
Wavicac R4
86 Retrosphenoverted cubatiapeiraticubatic honeycomb Rawvicac Great squarisquariapeirogonal tilings
Truncated cubes
Cuboctahedra
Wavicac R4
87 Apeiratidicubatic honeycomb Adach x4/3x4x4/3x4*a3o3*cØ*a *bØ*d Squarisquare tilings
Quasitruncated hexahedra
Truncated cubes
Wavicac R4
88 Retrotricubatic honeycomb Ratich x4x3o3/2x3*b4/3x4*d4/3*aØ*e Quasitruncated hexahedra
Truncated cubes
Cuboctatruncated cuboctahedra
Wavicac R4
89 Grand rhombic cubatiapeiratic honeycomb Garca Squarisquare tilings
Cuboctatruncated cuboctahedra
Wavicac R4
90 Dicubatiintercepted cubatiapeiratic honeycomb Dacanca Small squarisquariapeirogonal tilings
Truncated cubes
Cuboctahedra
Cuboctatruncated cuboctahedra
Wavicac R4
91 Cubatiintercepted cubatiapeiraticubatic honeycomb Cancoch Great squarisquariapeirogonal tilings
Quasitruncated hexahedra
Cuboctahedra
Cuboctatruncated cuboctahedra
Wavicac R4

Category 5: Greater Truncates[edit | edit source]

These are the great rhombates, great prismates (omnitruncates) and their kin. The vertex figures are various types of irregular tetrahedra.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
92 Great rhombated cubic honeycomb Grich o4x3x4x () Mirror-symmetric tetrahedron Great rhombicuboctahedra
Cubes
Truncated octahedra
Grich R4
93 Great rhombated tetrahedral-octahedral honeycomb Gratoh Mirror-symmetric tetrahedron Great rhombicuboctahedra
Truncated cubes
Truncated tetrahedra
Gratoh S4
94 Cubatitruncated cubatiapeiratic honeycomb Cuteca Mirror-symmetric tetrahedron Cuboctatruncated cuboctahedra
Truncated octahedra
Truncated square tilings
Cuteca R4
95 Dicubatitruncated apeiratic honeycomb Dacta Mirror-symmetric tetrahedron Squariapeirotruncated squariapeirogonal tilings
Truncated cubes
Quasitruncated hexahedra
Dacta R4
96 Great quasirhombated cubic honeycomb Gaqrich o4x3x4/3x () Mirror-symmetric tetrahedron Quasitruncated cuboctahedra
Cubes
Truncated octahedra
Gaqrich R4
97 Great quasirhombated tetrahedral-octahedral honeycomb Gaqratoh Mirror-symmetric tetrahedron Quasitruncated cuboctahedra
Quasitruncated hexahedra
Truncated tetrahedra
Gaqratoh S4
98 Cubatiquasitruncated cubatiapeiratic honeycomb Caquiteca o4x3x4x4/3*b Mirror-symmetric tetrahedron Cuboctatruncated cuboctahedra
Truncated octahedra
Quasitruncated square tilings
Caquiteca R4
99 Great prismated cubic honeycomb Gippich x4x3x4x () Phyllic disphenoid Great rhombicuboctahedra
Octagonal prisms
Gippich R4×2
100 Cubatitruncated prismatocubatiapeiratic honeycomb Cutpica Irregular tetrahedron Cuboctatruncated cuboctahedra
Great rhombicuboctahedra
Truncated square tilings
Octagrammic prisms
Cutpica R4
101 Great cubatitruncated prismatocubatiapeiratic honeycomb Gactipeca Irregular tetrahedron Cuboctatruncated cuboctahedra
Quasitruncated cuboctahedra
Quasirhombated square tilings
Octagrammic prisms
Gactipeca R4
102 Dicubatitruncated prismatoapeiratic honeycomb Dactapa Irregular tetrahedron Squariapeirotruncated squariapeirogonal tilings
Great rhombicuboctahedra
Quasitruncated cuboctahedra
Apeirogonal prisms
Dactapa R4
103 Cubatidicubatiapeiratic honeycomb Cadca Irregular tetrahedron Great rhombicuboctahedra
Quasitruncated cuboctahedra
Truncated octahedra
Quasirhombated square tilings
Cadca S4
104 Dicubatirhombated cubatihexagonal honeycomb Dicroch Irregular tetrahedron Cuboctatruncated cuboctahedra
Great rhombicuboctahedra
Quasitruncated cuboctahedra
Hexagonal tilings
Dicroch S4
105 Dicubatidiapeiratic honeycomb Dacda x4x4/3x4x4/3*a3*c *b~*d Phyllic disphenoid Cuboctatruncated cuboctahedra
Squariapeirotruncated squariapeirogonal tilings
Dacda R4×2
106 Great quasiprismated cubic honeycomb Gaquapech x4x3x4/3x () Irregular tetrahedron Great rhombicuboctahedra
Quasitruncated cuboctahedra
Octagonal prisms
Octagrammic prisms
Gaquapech R4
107 Quasiquasiprismated cubic honeycomb Quequapech x4/3x3x4/3x () Phyllic disphenoid Quasitruncated cuboctahedra
Octagrammic prisms
Quequapech R4×2
108 Cubatiquasitruncated prismatocubatiapeiratic honeycomb Caquitpica x4x3x4x4/3*b Irregular tetrahedron Cuboctatruncated cuboctahedra
Great rhombicuboctahedra
Quasirhombated square tilings
Octagonal prisms
Caquitpica R4
109 Great cubatiquasitruncated prismatocubatiapeiratic honeycomb Gacquitpica x4x3x4x4/3*b Irregular tetrahedron Cuboctatruncated cuboctahedra
Quasitruncated cuboctahedra
Quasitruncated square tilings
Octagonal prisms
Gacquitpica R4

Category 6: Prismatorhombates[edit | edit source]

These are the prismatorhombates (runcicantellates) and others with similar vertex figures, and their regiments. Their vertex figures are trapezoid pyramids.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
110 Prismatorhombated cubic honeycomb Prich x4o3x4x () Isosceles trapezoidal pyramid Small rhombicuboctahedra, Truncated cubes, Cubes, Octagonal prisms Prich R4
111 Small prismatodicubatiapeiratic honeycomb Sepdica Crossed isosceles trapezoidal pyramid Small cubicuboctahedra, Truncated cubes, Cubes, Truncated square tilings Prich R4
112 Small rhombiprismatocubatiapeiratic honeycomb Sirpaca Butterfly pyramid Small rhombihexahedra, Octagonal prisms, Truncated square tilings Prich R4
113 Quasiprismatorhombated cubic honeycomb Quiprich x4o3x4/3x () Isosceles trapezoidal pyramid Small rhombicuboctahedra, Quasitruncated hexahedra, Cubes, Octagrammic prisms Quiprich R4
114 Medial prismatodicubatiapeiratic honeycomb Mipdica Crossed isosceles trapezoidal pyramid Small cubicuboctahedra, Quasitruncated hexahedra, Cubes, Quasirhombated square tilings Quiprich R4
115 Medial rhombiprismatocubatiapeiratic honeycomb Mirpaca Butterfly pyramid Small rhombihexahedra, Octagrammic prisms, Quasirhombated square tilings Quiprich R4
116 Great prismatodicubatiapeiratic honeycomb Gepdica x4x3o4x4/3*b Isosceles trapezoidal pyramid Great cubicuboctahedra, Truncated cubes, Cubes, Quasirhombated square tilings Gepdica R4
117 Prismatoquasirhombated cubic honeycomb Paqrich x4x3o4/3x () Crossed isosceles trapezoidal pyramid Quasirhombicuboctahedra, Truncated cubes, Cubes, Octagonal prisms Gepdica R4
118 Great rhombiprismatocubatiapeiratic honeycomb Girpaca Butterfly pyramid Great rhombihexahedra, Octagonal prisms, Quasirhombated square tilings Gepdica R4
119 Grand prismatodicubatiapeiratic honeycomb Gapdica x4/3x3o4x4/3*b Isosceles trapezoidal pyramid Great cubicuboctahedra, Quasitruncated hexahedra, Cubes, Quasitruncated square tilings Gapdica R4
120 Quasiprismatoquasirhombated cubic honeycomb Quipqrich x4/3o3x4/3x () Crossed isosceles trapezoidal pyramid Quasirhombicuboctahedra, Quasitruncated hexahedra, Cubes, Octagrammic prisms Gapdica R4
121 Grand rhombiprismatocubatiapeiratic honeycomb Garpaca Butterfly pyramid Great rhombihexahedra, Octagrammic prisms, Quasitruncated square tilings Gapdica R4
122 Small cubatiprismatocubatiapeiratic honeycomb Sacpaca Isosceles trapezoidal pyramid Small squarisquariapeirogonal tilings, Truncated octahedra, Apeirogonal prisms, Quasitruncated cuboctahedra Sacpaca R4
123 Great cubatiprismatocubatiapeiratic honeycomb Gacpaca Crossed isosceles trapezoidal pyramid Great squarisquariapeirogonal tilings, Truncated octahedra, Apeirogonal prisms, Great rhombicuboctahedra Sacpaca R4
124 Rhombic apeirodicubatic honeycomb Radich Butterfly pyramid Squarisquare tilings, Quasitruncated cuboctahedra, Great rhombicuboctahedra Sacpaca R4
125 Dicubatiapeirocubatic honeycomb Dicach Trihexagonal tilings, Truncated cubes, Quasitruncated hexahedra, Cuboctatruncated cuboctahedra Dicach R4
126 Cubatiapeirodicubatic honeycomb Cadich x3o3/2x4/3x4*a~*c Triangular-hemiapeirogonal tilings, Truncated cubes, Quasitruncated hexahedra, Squariapeirotruncated squariapeirogonal tilings Dicach R4
127 Rhombic cubatidiapeiratic honeycomb Racda Hexagonal-hemiapeirogonal tilings, Cuboctatruncated cuboctahedra, Squariapeirotruncated squariapeirogonal tilings Dicach R4
128 Tricubatiapeiratic honeycomb Tica Cuboctahedra, Truncated cubes, Quasitruncated hexahedra, Quasirhombated square tilings Tica R4
129 Dicubatidicubatic honeycomb Dacdich x3o3/2x4/3x4*a3*c Octahemioctahedra, Truncated cubes, Quasitruncated hexahedra, Cuboctatruncated cuboctahedra Tica R4
130 Rhombic cubaticubatiapeiratic honeycomb Rocaca Cubohemioctahedra, Quasirhombated square tilings, Cuboctatruncated cuboctahedra Tica R4
131 Small tetracubatiapeirocubatic honeycomb Setcach Isosceles trapezoidal pyramid Small rhombicuboctahedra, Truncated tetrahedra, Quasitruncated square tilings, Quasitruncated cuboctahedra Setcach R4
132 Small dicubatitetraapeiratic honeycomb Sadcata x3o4/3x4/3x3*a4*c Crossed isosceles trapezoidal pyramid Small cubicuboctahedra, Truncated tetrahedra, Quasitruncated square tilings, Cuboctatruncated cuboctahedra Setcach R4
133 Small rhombic tricubatic honeycomb Sartich Butterfly pyramid Small rhombihexahedra, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Setcach R4
134 Great dicubatitetraapeiratic honeycomb Gadcata x3o4x4x3*a4/3*c Isosceles trapezoidal pyramid Great cubicuboctahedra, Truncated tetrahedra, Truncated square tilings, Cuboctatruncated cuboctahedra Gadcata R4
135 Great tetracubatiapeirocubatic honeycomb Getcach Crossed isosceles trapezoidal pyramid Quasirhombicuboctahedra, Truncated tetrahedra, Truncated square tilings, Great rhombicuboctahedra Gadcata R4
136 Great rhombic tricubatic honeycomb Gartich Butterfly pyramid Great rhombihexahedra, Cuboctatruncated cuboctahedra, Great rhombicuboctahedra Gadcata R4

Category 7: Triangular Podiumverts[edit | edit source]

These are the honeycombs with triangular podia or antipodia as their vertex figures, and their regiments.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
137 Dicubatihemiapeiratic honeycomb Dacha Cubes, Square-hemiapeirogonal tilings Chon
138 Disprismatohemiapeiratic honeycomb Dapha Cubes, Square-hemiapeirogonal tilings Chon
139 Spinoprismatocubatiapeiratic honeycomb Napca Cubes (two types), Square-hemiapeirogonal tilings Chon
140 Cyclotruncated tetrahedral-octahedral honeycomb Cytatoh x3x3o3o3*a () Triangular antiprism Tetrahedra, Truncated tetrahedra Cytatoh P4×2
141 Ditetrahemiapeiratic honeycomb Datha Tetrahedra, Triangular-hemiapeirogonal tilings Cytatoh P4×2
142 Inverted ditetrahemiapeiratic honeycomb Idatha Truncated tetrahedra, Triangular-hemiapeirogonal tilings Cytatoh P4×2
143 Tetratetraapeiratic honeycomb Tota Tetrahedra, Truncated tetrahedra, Trihexagonal tilings Cytatoh P4
144 Spinotetratetraapeiratic honeycomb Nateta Tetrahedra, Truncated tetrahedra, Hexagonal-hemiapeirogonal tilings Cytatoh P4
145 Great tetradicubatiapeiratic honeycomb Getdoca Tetrahedra, Cubes, Quasitruncated hexahedra, Quasitruncated square tilings Getdoca S4
146 Quasirhombated tetrahedral-octahedral honeycomb Qratoh Tetrahedra, Cubes, Quasirhombicuboctahedra Getdoca S4
147 Dicubatiapeiratic honeycomb Dacca Quasitruncated hexahedra, Quasitruncated square tilings, Quasirhombicuboctahedra Getdoca S4
148 Great cubatifaceted tetracubatiapeiratic honeycomb Gacoftaca Tetrahedra, Quasitruncated square tilings, Great cubicuboctahedra Getdoca S4
149 Great tetrafaceted cubatidicubatic honeycomb Gotafcadoch Cubes, Quasitruncated hexahedra, Great cubicuboctahedra Getdoca S4
150 Great spinotetradicubatic honeycomb Gantadoch Tetrahedra, Quasitruncated hexahedra, Great rhombihexahedra Getdoca S4
151 Great spinodicubatiapeiratic honeycomb Gandoca Cubes, Quasitruncated square tilings, Great rhombihexahedra Getdoca S4
152 Small rhombated tetrahedral-octahedral honeycomb Sratoh Triangular frustrum Tetrahedra, Cubes, Small rhombicuboctahedra Sratoh S4
153 Small tetradicubatiapeiratic honeycomb Stedoca Tetrahedra, Cubes, Truncated cubes, Truncated square tilings Sratoh S4
154 Cubatiapeirointercepted cubatic honeycomb Canach Truncated cubes, Truncated square tilings, Small rhombicuboctahedra Sratoh S4
155 Small cubatifaceted tetracubatiapeiratic honeycomb Scoftaca Tetrahedra, Truncated square tilings, Small cubicuboctahedra Sratoh S4
156 Small tetrafaceted cubatidicubatic honeycomb Stafcadoch Cubes, Truncated cubes, Small cubicuboctahedra Sratoh S4
157 Small spinotetradicubatic honeycomb Santadoch Tetrahedra, Truncated cubes, Small rhombihexahedra Sratoh S4
158 Small spinodicubatiapeiratic honeycomb Sandoca Cubes, Truncated square tilings, Small rhombihexahedra Sratoh S4

Category 8: Gacoca Regiment[edit | edit source]

Gacoca is the great cubaticubatiapeiratic honeycomb. Its regiment has 66 members whose vertex figures are facetings of a square podium (frustum).

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
159 Great cubaticubatiapeiratic honeycomb Gacoca Square podium Octahedra, Great cubicuboctahedra, Square tilings Gacoca R4
160 Small cubaticubatiapeiratic honeycomb Scoca o4o3x4x4/3*b Crossed square podium Octahedra, Small cubicuboctahedra, Square tilings Gacoca R4
161 Dicubicuboctahedral honeycomb Doccoh Great cubicuboctahedra, Small cubicuboctahedra Gacoca R4
162 Dirhombicuboctahedral honeycomb Dircoh Quasirhombicuboctahedra, Small rhombicuboctahedra Gacoca R4
163 Dirhombihexahedral honeycomb Drohah Great rhombihexahedra, Small rhombihexahedra Gacoca R4
164 Small octadicubatiapeiratic honeycomb Sodaca Octahedra, Quasirhombicuboctahedra, Small rhombihexahedra, Square tilings Gacoca R4
165 Great octadicubatiapeiratic honeycomb Godaca Octahedra, Great rhombihexahedra, Small rhombicuboctahedra, Square tilings Gacoca R4
166 Great spinoprismatocubatic honeycomb Gnappoch Great rhombihexahedra, Apeirogonal prisms Gacoca R4
167 Great spinodicubatic honeycomb Gandich Great rhombihexahedra, Cubes Gacoca R4
168 Small spinoprismatocubatic honeycomb Snappoch Small rhombihexahedra, Apeirogonal prisms Gacoca R4
169 Small spinodicubatic honeycomb Sandich Small rhombihexahedra, Cubes Gacoca R4
170 Small prismatodicubatic honeycomb Sapdoch Quasirhombicuboctahedra, Small cubicuboctahedra, Apeirogonal prisms Gacoca R4
171 Small cubatidicubatic honeycomb Sacdoch Quasirhombicuboctahedra, Small cubicuboctahedra, Cubes Gacoca R4
172 Great prismatodicubatic honeycomb Gapdoch Great cubicuboctahedra, Small rhombicuboctahedra, Apeirogonal prisms Gacoca R4
173 Great cubatidicubatic honeycomb Gacdoch Great cubicuboctahedra, Small rhombicuboctahedra, Cubes Gacoca R4
174 Small octaprismatocubatiapeiratic honeycomb Sopaca Octahedra, Small rhombicuboctahedra, Square tilings, Apeirogonal prisms Gacoca R4
175 Small octacubaticubatiapeiratic honeycomb Socaca Octahedra, Small rhombicuboctahedra, Square tilings, Cubes Gacoca R4
176 Great octaprismatocubatiapeiratic honeycomb Gopaca Octahedra, Quasirhombicuboctahedra, Square tilings, Apeirogonal prisms Gacoca R4
177 Great octacubaticubatiapeiratic honeycomb Gocaca Octahedra, Quasirhombicuboctahedra, Square tilings, Cubes Gacoca R4
178 Octadicubatiapeiratic honeycomb Odaca Octahedra, Quasirhombicuboctahedra, Small rhombicuboctahedra, Square tilings Gacoca S4
179 Small tricubatic honeycomb Satich Great cubicuboctahedra, Great rhombihexahedra, Small rhombicuboctahedra Gacoca S4
180 Great tricubatic honeycomb Gatich Quasirhombicuboctahedra, Small cubicuboctahedra, Small rhombihexahedra Gacoca S4
181 Octadicubatidicubatiapeiratic honeycomb Odicdica Octahedra, Great cubicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Small rhombihexahedra, Square tilings Gacoca S4
182 Cubatidicubatic honeycomb Cadoch Quasirhombicuboctahedra, Small rhombicuboctahedra, Cubes Gacoca S4
183 Prismatodicubatic honeycomb Padoch Quasirhombicuboctahedra, Small rhombicuboctahedra, Apeirogonal prisms Gacoca S4
184 Small octacubatitricubatiapeiratic honeycomb Soctica Octahedra, Great cubicuboctahedra, Great rhombihexahedra, Small rhombicuboctahedra, Cubes, Square tilings Gacoca S4
185 Small octaprismatotricubatiapeiratic honeycomb Soptica Octahedra, Great cubicuboctahedra, Great rhombihexahedra, Small rhombicuboctahedra, Apeirogonal prisms, Square tilings Gacoca S4
186 Great octacubatitricubatiapeiratic honeycomb Goctica Octahedra, Quasirhombicuboctahedra, Small cubicuboctahedra, Small rhombihexahedra, Cubes, Square tilings Gacoca S4
187 Great octaprismatotricubatiapeiratic honeycomb Goptica Octahedra, Quasirhombicuboctahedra, Small cubicuboctahedra, Small rhombihexahedra, Apeirogonal prisms, Square tilings Gacoca S4
188 Cubatidicubatidicubatic honeycomb Cadicdoch Great cubicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Small rhombihexahedra, Cubes Gacoca S4
189 Prismatodicubatidicubatic honeycomb Padicdoch Great cubicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Small rhombihexahedra, Apeirogonal prisms Gacoca S4
190 Sphenodicubatiapeiratic honeycomb Wadoca Great cubicuboctahedra, Small cubicuboctahedra, Squarisquare tilings Gacoca S4
191 Spinodicubatiapeiratic honeycomb Nadoca Great rhombihexahedra, Small rhombihexahedra, Squarisquare tilings Gacoca S4
192 Octadicubatidiapeiratic honeycomb Odacda Octahedra, Great cubicuboctahedra, Small cubicuboctahedra, Squarisquare tilings, Square tilings Gacoca S4
193 Great octacubatidicubatidiapeiratic honeycomb Gocdacda Octahedra, Great cubicuboctahedra, Quasirhombicuboctahedra, Small rhombihexahedra, Squarisquare tilings, Square tilings Gacoca S4
194 Small octacubatidicubatidiapeiratic honeycomb Socdacda Octahedra, Great rhombihexahedra, Small rhombicuboctahedra, Small cubicuboctahedra, Squarisquare tilings, Square tilings Gacoca S4
195 Retrodicubatidicubatiapeiratic honeycomb Rodacdica Great cubicuboctahedra, Quasirhombicuboctahedra, Small rhombicuboctahedra, Small cubicuboctahedra, Squarisquare tilings Gacoca S4
196 Invertidicubatidicubatiapeiratic honeycomb Idacdica Quasirhombicuboctahedra, Great rhombihexahedra, Small rhombicuboctahedra, Small rhombihexahedra, Squarisquare tilings Gacoca S4
197 Dicubaticubatiapeiratic honeycomb Dacoca Small rhombihexahedra, Great rhombihexahedra, Cubes, Squarisquare tilings Gacoca S4
198 Prismatocubaticubatiapeiratic honeycomb Pacoca Small rhombihexahedra, Great rhombihexahedra, Apeirogonal prisms, Squarisquare tilings Gacoca S4
199 Great cubaticubatidicubatiapeiratic honeycomb Gacocdica Quasirhombicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Cubes, Squarisquare tilings Gacoca S4
200 Great prismatocubatidicubatiapeiratic honeycomb Gapocdica Quasirhombicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Apeirogonal prisms, Squarisquare tilings Gacoca S4
201 Small cubaticubatidicubatiapeiratic honeycomb Scocdica Great cubicuboctahedra, Small rhombicuboctahedra, Small rhombihexahedra, Cubes, Squarisquare tilings Gacoca S4
202 Small prismatocubatidicubatiapeiratic honeycomb Spocdica Great cubicuboctahedra, Small rhombicuboctahedra, Small rhombihexahedra, Apeirogonal prisms, Squarisquare tilings Gacoca S4
203 Great octacubatitricubatidiapeiratic honeycomb Gocticda Octahedra, Great cubicuboctahedra, Quasirhombicuboctahedra, Small rhombihexahedra, Cubes, Squarisquare tilings, Square tilings Gacoca S4
204 Great octaprismatotricubatidiapeiratic honeycomb Gopticda Octahedra, Great cubicuboctahedra, Quasirhombicuboctahedra, Small rhombihexahedra, Apeirogonal prisms, Squarisquare tilings, Square tilings Gacoca S4
205 Small spinooctacubatitricubatidisapeiratic honeycomb Snocticda Octahedra, Great cubicuboctahedra, Small rhombicuboctahedra, Small rhombihexahedra, Cubes, Squarisquare tilings, Square tilings Gacoca S4
206 Small spinooctaprismatotricubatidisapeiratic honeycomb Snopticda Octahedra, Great cubicuboctahedra, Small rhombicuboctahedra, Small rhombihexahedra, Apeirogonal prisms, Squarisquare tilings, Square tilings Gacoca S4
207 Great spinooctacubatitricubatidisapeiratic honeycomb Ganocticda Octahedra, Quasirhombicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Cubes, Squarisquare tilings, Square tilings Gacoca S4
208 Great spinooctaprismatotricubatidisapeiratic honeycomb Ganopticda Octahedra, Quasirhombicuboctahedra, Great rhombihexahedra, Small cubicuboctahedra, Apeirogonal prisms, Squarisquare tilings, Square tilings Gacoca S4
209 Small octacubatitricubatidiapeiratic honeycomb Socticda Octahedra, Great rhombihexahedra, Small rhombicuboctahedra, Small cubicuboctahedra, Cubes, Squarisquare tilings, Square tilings Gacoca S4
210 Small octaprismatotricubatidiapeiratic honeycomb Sopticda Octahedra, Great rhombihexahedra, Small rhombicuboctahedra, Small cubicuboctahedra, Apeirogonal prisms, Squarisquare tilings, Square tilings Gacoca S4
211 Great hemihexacubatiapeiratihemiapeiratic honeycomb Ghahocaha Tetrahemihexahedra, Great cubicuboctahedra, Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
212 Small hemihexacubatiapeiratihemiapeiratic honeycomb Shahocaha Tetrahemihexahedra, Small cubicuboctahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
213 Great hemihexacubatidicubatiapeiratihemiapeiratic honeycomb Ghahcdicaha Tetrahemihexahedra, Great cubicuboctahedra (two types), Small cubicuboctahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
214 Small hemihexacubatidicubatiapeiratihemiapeiratic honeycomb Shahcdicaha Tetrahemihexahedra, Great cubicuboctahedra, Small cubicuboctahedra (two types), Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
215 Great hemihexadicubatiapeiratihemiapeiratic honeycomb Ghahdicaha Tetrahemihexahedra, Quasirhombicuboctahedra, Small rhombihexahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
216 Small hemihexadicubatiapeiratihemiapeiratic honeycomb Shahdicaha Tetrahemihexahedra, Great rhombihexahedra, Small rhombicuboctahedra, Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
217 Great hemihexatricubatiapeiratihemiapeiratic honeycomb Ghahticaha Tetrahemihexahedra, Great cubicuboctahedra, Great rhombihexahedra, Small rhombihexahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
218 Small hemihexatricubatiapeiratihemiapeiratic honeycomb Shahticaha Tetrahemihexahedra, Great rhombihexahedra, Small cubicuboctahedra, Small rhombihexahedra, Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
219 Great hemihexadicubaticubatiapeiratihemiapeiratic honeycomb Ghahdicocaha Tetrahemihexahedra, Great cubicuboctahedra, Quasirhombicuboctahedra, Small rhombicuboctahedra,Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
220 Small hemihexadicubaticubatiapeiratihemiapeiratic honeycomb Shahdicocaha Tetrahemihexahedra, Quasirhombicuboctahedra, Small rhombicuboctahedra, Small cubicuboctahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
221 Great hemihexacubatitricubatiapeiratihemiapeiratic honeycomb Ghahcticaha Tetrahemihexahedra, Quasirhombicuboctahedra (two types), Small rhombicuboctahedra, Small rhombihexahedra, Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
222 Small hemihexacubatitricubatiapeiratihemiapeiratic honeycomb Shahcticaha Tetrahemihexahedra, Quasirhombicuboctahedra, Great rhombihexahedra, Small rhombicuboctahedra (two types), Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
223 Great hemihexadicubatidicubatiapeiratihemiapeiratic honeycomb Ghahdicdicaha Tetrahemihexahedra, Quasirhombicuboctahedra, Great rhombihexahedra, Small rhombihexahedra (two types), Small squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4
224 Small hemihexadicubatidicubatiapeiratihemiapeiratic honeycomb Shahdicdicaha Tetrahemihexahedra, Great rhombihexahedra (two types), Small rhombicuboctahedra, Small rhombihexahedra, Great squarisquariapeirogonal tilings, Square-hemiapeirogonal tilings Gacoca S4

Category 9: Skewverts[edit | edit source]

These are the honeycombs with skewed wedges as vertex figures, and their regiments.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
225 Small skewverted dicubatidicubatic honeycomb Skivdacdich x3x3/2o4/3x4*a3*c Small rhombicuboctahedra, Small cubicuboctahedra, Octahemioctahedra, Great rhombicuboctahedra Srich S4
226 Small skewverted tricubaticubic honeycomb Skivticach Small rhombihexahedra, Cubohemioctahedra, Cubes, Great rhombicuboctahedra Srich S4
227 Small skewverted tricubatiapeiratic honeycomb Skivtica Small rhombihexahedra, Cubohemioctahedra, Truncated square tilings, Great rhombicuboctahedra Srich S4
228 Small skewverted dicubatitricubatiapeiratic honeycomb Skiv dactica Small cubicuboctahedra, Small rhombicuboctahedra, Octahemioctahedra, Cubes, Truncated square tilings, Great rhombicuboctahedra Srich S4
229 Great skewverted dicubatidicubatic honeycomb Gikkivdacdich x3x3/2o4x4/3*a3*c Quasirhombicuboctahedra, Great cubicuboctahedra, Octahemioctahedra, Quasitruncated cuboctahedra Wavicoca S4
230 Great skewverted tricubatiapeiratic honeycomb Gikkivtica Great rhombihexahedra, Cubohemioctahedra, Quasitruncated square tilings, Quasitruncated cuboctahedra Wavicoca S4
231 Great skewverted tricubaticubic honeycomb Gikvaticach Great rhombihexahedra, Cubohemioctahedra, Cubes, Quasitruncated cuboctahedra Wavicoca S4
232 Great skewverted dicubatitricubatiapeiratic honeycomb Gikkiv dactica Quasirhombicuboctahedra, Great cubicuboctahedra, Octahemioctahedra, Cubes, Quasitruncated square tilings, Quasitruncated cuboctahedra Wavicoca S4
233 Small skewverted prismatocubaticubatiapeiratic honeycomb Skivpacoca Great cubicuboctahedra, Small rhombicuboctahedra, Square tilings, Octagrammic prisms Skivpacoca R4
234 Skewverted dicubatidiapeiratic honeycomb Kavidacda x4x4/3o4x4/3*a3*c *b~*d Great cubicuboctahedra, Small cubicuboctahedra, Square-hemiapeirogonal tilings, Squariapeirotruncated squariapeirogonal tilings Skivpacoca R4
235 Great skewverted prismatocubaticubatiapeiratic honeycomb Gikkivpacoca x4/3o3x4x4/3*b Quasirhombicuboctahedra, Small cubicuboctahedra, Square tilings, Octagonal prisms Skivpacoca R4
236 Skewverted prismatodicubatiapeiratic honeycomb Kevpadoca Quasirhombicuboctahedra, Small rhombicuboctahedra, Square-hemiapeirogonal tilings, Apeirogonal prisms Skivpacoca R4
237 Small skewverted prismatocubatidiapeiratic honeycomb Skivpacda Small rhombihexahedra, Square-hemiapeirogonal tilings, Squariapeirotruncated squariapeirogonal tilings, Octagrammic prisms Skivpacoca R4
238 Skewverted disprismatodicubatic honeycomb Kavadipdich Great rhombihexahedra, Small rhombihexahedra, Octagrammic prisms, Octagonal prisms Skivpacoca R4
239 Small skewverted disprismatocubatiapeiratic honeycomb Skivdapoca Great rhombihexahedra, Square-hemiapeirogonal tilings, Apeirogonal prisms, Octagrammic prisms Skivpacoca R4
240 Skewverted trisprismatoapeiratic honeycomb Kivtipa Squariapeirotruncated squariapeirogonal tilings, Octagrammic prisms, Octagonal prisms, Apeirogonal prisms Skivpacoca R4
241 Great skewverted disprismatocubatiapeiratic honeycomb Gikkivdapoca Small rhombihexahedra, Square-hemiapeirogonal tilings, Apeirogonal prisms, Octagonal prisms Skivpacoca R4
242 Skewverted prismatocubaticubatiapeiratic honeycomb Kevpacoca Great rhombihexahedra, Small rhombihexahedra, Squariapeirotruncated squariapeirogonal tilings, Apeirogonal prisms Skivpacoca R4
243 Great skewverted prismatocubatidiapeiratic honeycomb Gikkivpacda Great rhombihexahedra, Square-hemiapeirogonal tilings, Squariapeirotruncated squariapeirogonal tilings, Octagonal prisms Skivpacoca R4
244 Small skewverted disprismatodicubatidiapeiratic honeycomb Skiv dapdocda Great cubicuboctahedra, Small rhombicuboctahedra, Square tilings, Squariapeirotruncated squariapeirogonal tilings, Apeirogonal prisms, Octagonal prisms Skivpacoca R4
245 Skewverted trisprismatodicubatiapeiratic honeycomb Kevtipdoca Great cubicuboctahedra, Small cubicuboctahedra, Square-hemiapeirogonal tilings, Apeirogonal prisms, Octagrammic prisms, Octagonal prisms Skivpacoca R4
246 Great skewverted disprismatodicubatidiapeiratic honeycomb Gikkiv dapdocda Quasirhombicuboctahedra, Small cubicuboctahedra, Square tilings, Squariapeirotruncated squariapeirogonal tilings, Apeirogonal prisms, Octagrammic prisms Skivpacoca R4
247 Skewverted disprismatodicubatidiapeiratic honeycomb Kivdapdocda Quasirhombicuboctahedra, Small rhombicuboctahedra, Square-hemiapeirogonal tilings, Squariapeirotruncated squariapeirogonal tilings, Octagrammic prisms, Octagonal prisms Skivpacoca R4
248 Small skewverted cubatiapeiratidicubatic honeycomb Skivcadach Great cubicuboctahedra, Small rhombicuboctahedra, Trihexagonal tilings, Quasitruncated cuboctahedra Skivcadach S4
249 Skewverted cubatiapeiraticubatiapeiratic honeycomb Kevcaca x4/3x4x3/2o3*a~*c *b4*d Great cubicuboctahedra, Small cubicuboctahedra, Triangular-hemiapeirogonal tilings, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4
250 Great skewverted cubatiapeiratidicubatic honeycomb Gikkivcadach Quasirhombicuboctahedra, Small cubicuboctahedra, Trihexagonal tilings, Great rhombicuboctahedra Skivcadach S4
251 Skewverted prismatocubatiapeiraticubatic honeycomb Kivpocach Quasirhombicuboctahedra, Small rhombicuboctahedra, Triangular-hemiapeirogonal tilings, Apeirogonal prisms Skivcadach S4
252 Small skewverted diapeiratidicubatic honeycomb Skivdadoch Great rhombihexahedra, Hexagonal-hemiapeirogonal tilings, Quasitruncated cuboctahedra, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4
253 Skewverted dicubatidicubatic honeycomb Kevdacdich Great rhombihexahedra, Small rhombihexahedra, Quasitruncated cuboctahedra, Great rhombicuboctahedra Skivcadach S4
254 Small skewverted prismatoapeiratidicubatic honeycomb Skivpadoch Small rhombihexahedra, Hexagonal-hemiapeirogonal tilings, Apeirogonal prisms, Quasitruncated cuboctahedra Skivcadach S4
255 Skewverted prismatoapeiraticubaticubatic honeycomb Kevpacoch Squariapeirotruncated squariapeirogonal tilings, Quasitruncated cuboctahedra, Great rhombicuboctahedra, Apeirogonal prisms Skivcadach S4
256 Great skewverted prismatoapeiratidicubatic honeycomb Gikkivpadoch Great rhombihexahedra, Hexagonal-hemiapeirogonal tilings, Apeirogonal prisms, Great rhombicuboctahedra Skivcadach S4
257 Skewverted prismatotriscubatic honeycomb Kaviptich Great rhombihexahedra, Small rhombihexahedra, Squariapeirotruncated squariapeirogonal tilings, Apeirogonal prisms Skivcadach S4
258 Great skewverted diapeiratidicubatic honeycomb Gikkivdadoch Small rhombihexahedra, Hexagonal-hemiapeirogonal tilings, Great rhombicuboctahedra, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4
259 Small skewverted prismatodiapeiraticubatidicubatic honeycomb Skiv pidacdoch Great cubicuboctahedra, Small rhombicuboctahedra, Trihexagonal tilings, Great rhombicuboctahedra, Apeirogonal prisms, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4
260 Skewverted prismatodicubatidicubatiapeiratic honeycomb Kevpadicdoca Great cubicuboctahedra, Small cubicuboctahedra, Triangular-hemiapeirogonal tilings, Quasitruncated cuboctahedra, Great rhombicuboctahedra, Apeirogonal prisms Skivcadach S4
261 Great skewverted prismatodiapeiraticubatidicubatic honeycomb Gikkiv pidacdoch Quasirhombicuboctahedra, Small cubicuboctahedra, Trihexagonal tilings, Quasitruncated cuboctahedra, Apeirogonal prisms, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4
262 Skewverted dicubatidicubatidiapeiratic honeycomb Kevdacdicda Quasirhombicuboctahedra, Small rhombicuboctahedra, Trihexagonal tilings, Quasitruncated cuboctahedra, Great rhombicuboctahedra, Squariapeirotruncated squariapeirogonal tilings Skivcadach S4

Category 10: Ditetrahedronaries[edit | edit source]

These are the members of the octet regiment with cyclotettic symmetry. They have tetrahedrally symmetric vertex figures.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
263 Ditetrahedronary tetrahemiapeiratic honeycomb Datteha Antitruncated tetrahedron Tetrahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
264 Ditetrahedronary tetraoctahemiapeiratic honeycomb Dattoha x3/2o3o3o3/2*a∞o3*b *dØ*e Tetrahedra, Octahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
265 Ditetrahedronary tetratomotetrahemihexagonal honeycomb Dattetuthah Tetrahedra, Truncated tetrahedra, Hexagonal tilings Octet P4
266 Ditetrahedronary tetraoctatomotetrahemihexagonal honeycomb Dattotuthah Tetrahedra, Octahedra, Truncated tetrahedra, Hexagonal tilings Octet P4
267 Ditetrahedronary tetracuboctahemiapeiratic honeycomb Datetcoha Tetrahedra, Cuboctahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
268 Ditetrahedronary tetratomotetracuboctahemihexagonal honeycomb Datet tocohaht Tetrahedra, Truncated tetrahedra, Cuboctahedra, Hexagonal tilings Octet P4
269 Ditetrahedronary tomotetrahemioctahemiapeiratic honeycomb Dattuthoha Truncated tetrahedra, Octahemioctahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
270 Ditetrahedronary tetratomotetrahemioctahedral honeycomb Datetutho Tetrahedra, Truncated tetrahedra, Octahemioctahedra Octet P4
271 Retroditetrahedronary tetratomotetrahemioctahedral honeycomb Radtetutho Tetrahedra, Truncated tetrahedra, Cubohemioctahedra Octet P4
272 Retroditetrahedronary tomotetrahemioctahemiapeiratic honeycomb Radtatuthoha Truncated tetrahedra, Cubohemioctahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
273 Ditetrahedronary octatomotetrahemioctahemiapeiratic honeycomb Datotuthoha Octahedra, Truncated tetrahedra, Cubohemioctahedra, Ditrigonary triangular-hemiapeirogonal tilings Octet P4
274 Ditetrahedronary tetratomotetrahemioctahemitriangular honeycomb Datet tuthoth Tetrahedra, Truncated tetrahedra, Cubohemioctahedra, Triangular tilings Octet P4
275 Ditetrahedronary tetraoctatomotetrahemioctahedral honeycomb Dattotutho Tetrahedra, Octahedra, Truncated tetrahedra, Cubohemioctahedra Octet P4
276 Ditetrahedronary tetrahemihexahemisquare honeycomb Datethahsh () /2 Tetrahedra, Tetrahemihexahedra, Square tilings Octet P4
277 Ditetrahedronary tetrahemihexahemitriangular hemisquare honeycomb Datet hahthash Tetrahedra, Tetrahemihexahedra, Triangular tilings, Square tilings Octet P4
278 Ditetrahedronary hemihexahemisquare hemiapeiratic honeycomb Dathahasha Tetrahemihexahedra, Ditrigonary triangular-hemiapeirogonal tilings, Square tilings Octet P4
279 Ditetrahedronary tetradistomotetrahemihexahemisquare honeycomb Datet dituthahash Tetrahedra, Truncated tetrahedra (two types), Tetrahemihexahedra, Square tilings Octet P4
280 Ditetrahedronary distomotetrahemihexahemiapeiratihemisquare honeycomb Datdut thahasha Truncated tetrahedra (two types), Tetrahemihexahedra, Ditrigonary triangular-hemiapeirogonal tilings, Square tilings Octet P4
281 Ditetrahedronary tomotetrahemihexahemihexagonal hemisquare honeycomb Dattut hahahash Truncated tetrahedra, Tetrahemihexahedra, Hexagonal tilings, Square tilings Octet P4
282 Ditetrahedronary tomotetrahemioctahemihexahemisquare honeycomb Dattutho hahash Truncated tetrahedra, Octahemioctahedra, Tetrahemihexahedra, Square tilings Octet P4
283 Ditetrahedronary tetrahemioctahemihexahemihexagonal hemisquare honeycomb Datetho hahahash Tetrahedra, Octahemioctahedra, Tetrahemihexahedra, Hexagonal tilings, Square tilings Octet P4

Category 11: Stut Cadoca Regiment[edit | edit source]

Stut cadoca is the small tritrigonary cubatidicubatiapeiratic honeycomb. Its regiment has 79 members whose vertices are facetings of a triangular cupola with a regular hexagon base.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
284 Small tritrigonary cubatidicubatiapeiratic honeycomb Stut cadoca Triangular cupola Cubes, Triangular tilings, Great cubicuboctahedra, Quasitruncated hexahedra Stut cadoca S4
285 Small tritrigonary dicubatidiapeiratic honeycomb Stut dacda o3o3/2x4/3x4*a~*c Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Quasitruncated hexahedra, Small squarisquariapeirogonal tilings Stut cadoca S4
286 Great tritrigonary cubatidicubatiapeiratic honeycomb Getit cadoca Cubes, Triangular tilings, Small cubicuboctahedra, Truncated cubes Stut cadoca S4
287 Great tritrigonary dicubatidiapeiratic honeycomb Getit dacda o3o3/2x4x4/3*a~*c Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great squarisquariapeirogonal tilings, Truncated cubes Stut cadoca S4
288 Small tritrigonary prismatodicubatiapeiratic honeycomb Stut padoca Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Quasirhombicuboctahedra, Apeirogonal prisms Stut cadoca S4
289 Great tritrigonary prismatodicubatiapeiratic honeycomb Getit padoca Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Small rhombicuboctahedra, Apeirogonal prisms Stut cadoca S4
290 Small tritrigonary cubatidiapeiratic honeycomb Stutacda Ditrigonary triangular-hemiapeirogonal tilings, Great cubicuboctahedra, Small squarisquariapeirogonal tilings Stut cadoca S4
291 Great tritrigonary cubatidiapeiratic honeycomb Getitacda Ditrigonary triangular-hemiapeirogonal tilings, Great squarisquariapeirogonal tilings, Small cubicuboctahedra Stut cadoca S4
292 Tritrigonary dicubatiapeiratic honeycomb Titdoca Triangular tilings, Quasirhombicuboctahedra, Small rhombicuboctahedra Stut cadoca S4
293 Small tritrigonary cubatitricubatic honeycomb Stut catich Cubes, Quasirhombicuboctahedra, Small rhombihexahedra, Truncated cubes Stut cadoca S4
294 Small tritrigonary prismatocubaticubatiapeiratic honeycomb Stut pacoca Cubes, Great squarisquariapeirogonal tilings, Small rhombihexahedra, Apeirogonal prisms Stut cadoca S4
295 Small tritrigonary prismatocubatiapeiraticubatic honeycomb Stut pocach Quasirhombicuboctahedra, Great squarisquariapeirogonal tilings, Truncated cubes, Apeirogonal prisms Stut cadoca S4
296 Great tritrigonary cubatitricubatic honeycomb Getit catich Cubes, Great rhombihexahedra, Quasitruncated hexahedra, Small rhombicuboctahedra Stut cadoca S4
297 Great tritrigonary prismatocubatiapeiraticubatic honeycomb Getit pocach Quasitruncated hexahedra, Small squarisquariapeirogonal tilings, Small rhombicuboctahedra, Apeirogonal prisms Stut cadoca S4
298 Great tritrigonary prismatocubaticubatiapeiratic honeycomb Getit pacoca Cubes, Great rhombihexahedra, Small squarisquariapeirogonal tilings, Apeirogonal prisms Stut cadoca S4
299 Tritrigonary dicubatidicubatic honeycomb Titdacdoch Great cubicuboctahedra, Quasitruncated hexahedra, Small cubicuboctahedra, Truncated cubes Stut cadoca S4
300 Small tritrigonary dicubaticubatiapeiratic honeycomb Stut dacoca Cubes, Quasitruncated hexahedra, Squarisquare tilings, Small cubicuboctahedra Stut cadoca S4
301 Great tritrigonary dicubaticubatiapeiratic honeycomb Getit dacoca Cubes, Great cubicuboctahedra, Squarisquare tilings, Truncated cubes Stut cadoca S4
302 Small tritrigonary prismatodicubatidiapeiratic honeycomb Stut padicda Triangular tilings, Great squarisquariapeirogonal tilings, Small rhombicuboctahedra, Truncated cubes, Apeirogonal prisms Stut cadoca S4
303 Small tritrigonary prismatotricubatiapeiratic honeycomb Stut patoca Ditrigonary triangular-hemiapeirogonal tilings, Quasirhombicuboctahedra, Small cubicuboctahedra, Truncated cubes, Apeirogonal prisms Stut cadoca S4
304 Small tritrigonary dicubatiprismatoapeiratic honeycomb Stut dacopa Ditrigonary triangular-hemiapeirogonal tilings, Small rhombihexahedra, Truncated cubes, Apeirogonal prisms Stut cadoca S4
305 Great tritrigonary prismatodicubatidiapeiratic honeycomb Getit padicda Triangular tilings, Quasirhombicuboctahedra, Quasitruncated hexahedra, Small squarisquariapeirogonal tilings, Apeirogonal prisms Stut cadoca S4
306 Great tritrigonary dicubatiprismatoapeiratic honeycomb Getit dacopa Ditrigonary triangular-hemiapeirogonal tilings, Great rhombihexahedra, Quasitruncated hexahedra, Apeirogonal prisms Stut cadoca S4
307 Great tritrigonary prismatotricubatiapeiratic honeycomb Getit patoca Ditrigonary triangular-hemiapeirogonal tilings, Great cubicuboctahedra, Quasitruncated hexahedra, Small rhombicuboctahedra, Apeirogonal prisms Stut cadoca S4
308 Tritrigonary dicubatidiapeiratic honeycomb Titdacda Triangular tilings, Quasitruncated hexahedra, Squarisquare tilings, Truncated cubes Stut cadoca S4
309 Great tritrigonary tricubatidiapeiratic honeycomb Getit tacda Ditrigonary triangular-hemiapeirogonal tilings, Great cubicuboctahedra, Quasitruncated hexahedra, Great squarisquariapeirogonal tilings, Truncated cubes Stut cadoca S4
310 Small tritrigonary tricubatidiapeiratic honeycomb Stut tacda Ditrigonary triangular-hemiapeirogonal tilings, Quasitruncated hexahedra, Small squarisquariapeirogonal tilings, Small cubicuboctahedra, Truncated cubes Stut cadoca S4
311 Tritrigonary dicubatidicubatiapeiratic honeycomb Totdicdica Triangular tilings, Great rhombihexahedra, Quasitruncated hexahedra, Small rhombihexahedra, Truncated cubes Stut cadoca S4
312 Small tritrigonary dicubatiprismatodiapeiratic honeycomb Stut dacpada Ditrigonary triangular-hemiapeirogonal tilings, Quasitruncated hexahedra, Squarisquare tilings, Small rhombihexahedra, Apeirogonal prisms Stut cadoca S4
313 Great tritrigonary dicubatiprismatodiapeiratic honeycomb Getit dacpada Ditrigonary triangular-hemiapeirogonal tilings, Great rhombihexahedra, Squarisquare tilings, Truncated cubes, Apeirogonal prisms Stut cadoca S4
314 Small tritrigonary tetriscubatidiapeiratic honeycomb Stut tucda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great rhombihexahedra, Quasitruncated hexahedra, Great squarisquariapeirogonal tilings, Small rhombihexahedra Stut cadoca S4
315 Small tritrigonary cubatitricubatidiapeiratic honeycomb Stut caticda Cubes, Triangular tilings, Quasirhombicuboctahedra, Quasitruncated hexahedra, Squarisquare tilings, Small rhombihexahedra Stut cadoca S4
316 Great tritrigonary tetriscubatidiapeiratic honeycomb Getit tucda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great rhombihexahedra, Small squarisquariapeirogonal tilings, Small rhombihexahedra, Truncated cubes Stut cadoca S4
317 Great tritrigonary cubatitricubatidiapeiratic honeycomb Getit caticda Cubes, Triangular tilings, Great rhombihexahedra, Squarisquare tilings, Small rhombicuboctahedra, Truncated cubes Stut cadoca S4
318 Small tritrigonary prismatotricubatidiapeiratic honeycomb Stut paticda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great cubicuboctahedra, Squarisquare tilings, Small rhombihexahedra, Apeirogonal prisms Stut cadoca S4
319 Great tritrigonary prismatotricubatidiapeiratic honeycomb Getit paticda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great rhombihexahedra, Squarisquare tilings, Small cubicuboctahedra, Apeirogonal prisms Stut cadoca S4
320 Toroidotritrigonary dicubatiapeiratic honeycomb Totitdoca Great rhombihexahedra, Squarisquare tilings, Small rhombihexahedra Stut cadoca S4
321 Small tritrigonary dicubatiapeiratic honeycomb Stutdica Hexagonal tilings, Great rhombihexahedra, Quasitruncated cuboctahedra Stut cadoca S4
322 Tritrigonary cubatidiapeiratic honeycomb Titcada Hexagonal tilings, Squarisquare tilings, Cuboctatruncated cuboctahedra Stut cadoca S4
323 Great tritrigonary dicubatiapeiratic honeycomb Getitdica Hexagonal tilings, Small rhombihexahedra, Great rhombicuboctahedra Stut cadoca S4
324 Small tritrigonary cubatidicubatic honeycomb Stutcadoch Great rhombihexahedra, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
325 Tritrigonary cubatiapeiraticubatic honeycomb Titcach Squarisquare tilings, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
326 Great tritrigonary cubatidicubatic honeycomb Getitcadoch Small rhombihexahedra, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
327 Small tritrigonary cubatitricubatiapeiratic honeycomb Stut catoca Cubes, Hexagonal tilings, Quasitruncated hexahedra, Small rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
328 Small tritrigonary prismatocubaticubatidiapeiratic honeycomb Stut pacocda Cubes, Hexagonal tilings, Small squarisquariapeirogonal tilings, Apeirogonal prisms, Quasitruncated cuboctahedra Stut cadoca S4
329 Small tritrigonary tricubaticubatiapeiratic honeycomb Stut tacoca Cubes, Hexagonal tilings, Quasitruncated hexahedra, Small cubicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
330 Great tritrigonary tricubaticubatiapeiratic honeycomb Getit tacoca Cubes, Hexagonal tilings, Small squarisquariapeirogonal tilings, Truncated cubes, Cuboctatruncated cuboctahedra Stut cadoca S4
331 Great tritrigonary prismatocubaticubatidiapeiratic honeycomb Getit pacocda Cubes, Hexagonal tilings, Great squarisquariapeirogonal tilings, Apeirogonal prisms, Great rhombicuboctahedra Stut cadoca S4
332 Great tritrigonary cubatitricubatiapeiratic honeycomb Getit catoca Cubes, Hexagonal tilings, Quasirhombicuboctahedra, Truncated cubes, Great rhombicuboctahedra Stut cadoca S4
333 Small tritrigonary dicubatidicubatidiapeiratic honeycomb Stut dacdicda Cubes, Hexagonal tilings, Quasirhombicuboctahedra, Squarisquare tilings, Truncated cubes, Quasitruncated cuboctahedra Stut cadoca S4
334 Small tritrigonary dicubatitricubatiapeiratic honeycomb Stut dactica Cubes, Hexagonal tilings, Great cubicuboctahedra, Small rhombihexahedra, Truncated cubes, Quasitruncated cuboctahedra Stut cadoca S4
335 Small tritrigonary prismatocubatidicubatidiapeiratic honeycomb Stut pacdicda Cubes, Hexagonal tilings, Great rhombihexahedra, Great squarisquariapeirogonal tilings, Apeirogonal prisms, Cuboctatruncated cuboctahedra Stut cadoca S4
336 Great tritrigonary prismatocubatidicubatidiapeiratic honeycomb Getit pacdicda Cubes, Hexagonal tilings, Small squarisquariapeirogonal tilings, Small rhombihexahedra, Apeirogonal prisms, Cuboctatruncated cuboctahedra Stut cadoca S4
337 Great tritrigonary dicubatitricubatiapeiratic honeycomb Getit dactica Cubes, Hexagonal tilings, Great rhombihexahedra, Quasitruncated hexahedra, Small cubicuboctahedra, Great rhombicuboctahedra Stut cadoca S4
338 Great tritrigonary dicubatidicubatidiapeiratic honeycomb Getit dacdicda Cubes, Hexagonal tilings, Quasitruncated hexahedra, Squarisquare tilings, Small rhombicuboctahedra, Great rhombicuboctahedra Stut cadoca S4
339 Small tritrigonary tricubatidicubatiapeiratic honeycomb Stut tacdica Hexagonal tilings, Quasirhombicuboctahedra, Quasitruncated hexahedra, Small cubicuboctahedra, Truncated cubes, Quasitruncated cuboctahedra Stut cadoca S4
340 Small tritrigonary prismatotetriscubatiapeiratic honeycomb Stut putca Hexagonal tilings, Great cubicuboctahedra, Great squarisquariapeirogonal tilings, Truncated cubes, Apeirogonal prisms, Quasitruncated cuboctahedra Stut cadoca S4
341 Small tritrigonary prismatocubatitricubatiapeiratic honeycomb Stut pactica Hexagonal tilings, Quasitruncated hexahedra, Great squarisquariapeirogonal tilings, Small rhombicuboctahedra, Apeirogonal prisms, Cuboctatruncated cuboctahedra Stut cadoca S4
342 Great tritrigonary prismatocubatitricubatiapeiratic honeycomb Getit pactica Hexagonal tilings, Quasirhombicuboctahedra, Small squarisquariapeirogonal tilings, Truncated cubes, Apeirogonal prisms, Cuboctatruncated cuboctahedra Stut cadoca S4
343 Great tritrigonary prismatotetriscubatiapeiratic honeycomb Getit putca Hexagonal tilings, Quasitruncated hexahedra, Small squarisquariapeirogonal tilings, Small cubicuboctahedra, Apeirogonal prisms, Great rhombicuboctahedra Stut cadoca S4
344 Great tritrigonary tricubatidicubatiapeiratic honeycomb Getit tacdica Hexagonal tilings, Great cubicuboctahedra, Quasitruncated hexahedra, Small rhombicuboctahedra, Truncated cubes, Great rhombicuboctahedra Stut cadoca S4
345 Small tritrigonary dicubatitricubatic honeycomb Stut dactoch Cubes, Quasitruncated hexahedra, Small rhombicuboctahedra, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
346 Small tritrigonary tetriscubatiapeiratic honeycomb Stut tuca Cubes, Small squarisquariapeirogonal tilings, Apeirogonal prisms, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
347 Small tritrigonary tricubatidicubatic honeycomb Stut tacdoch Cubes, Quasitruncated hexahedra, Small cubicuboctahedra, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
348 Great tritrigonary tricubatidicubatic honeycomb Getit tacdoch Cubes, Great cubicuboctahedra, Truncated cubes, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
349 Great tritrigonary tetriscubatiapeiratic honeycomb Getit tuca Cubes, Great squarisquariapeirogonal tilings, Apeirogonal prisms, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
350 Great tritrigonary dicubatitricubatic honeycomb Getit dactoch Cubes, Quasirhombicuboctahedra, Truncated cubes, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
351 Tritrigonary cubatitricubatiapeiratic honeycomb Tatcatica Triangular tilings, Quasitruncated hexahedra, Truncated cubes, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
352 Small tritrigonary cubatiprismatodicubatiapeiratic honeycomb Stut capdoca Ditrigonary triangular-hemiapeirogonal tilings, Quasitruncated hexahedra, Apeirogonal prisms, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
353 Great tritrigonary cubatiprismatodicubatiapeiratic honeycomb Getit capdoca Ditrigonary triangular-hemiapeirogonal tilings, Truncated cubes, Apeirogonal prisms, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
354 Small tritrigonary tetriscubaticubatiapeiratic honeycomb Stut tucoca Cubes, Triangular tilings, Small rhombicuboctahedra, Truncated cubes, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
355 Small tritrigonary cubaticubatidicubatidiapeiratic honeycomb Stut cacdicda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Quasitruncated hexahedra, Great squarisquariapeirogonal tilings, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
356 Small tritrigonary prismatotetriscubatiapeiratic honeycomb Stut patuca Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Great cubicuboctahedra, Apeirogonal prisms, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
357 Great tritrigonary tetriscubaticubatiapeiratic honeycomb Getit tucoca Cubes, Triangular tilings, Quasirhombicuboctahedra, Quasitruncated hexahedra, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
358 Great tritrigonary prismatotetriscubatiapeiratic honeycomb Getit patuca Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Small cubicuboctahedra, Apeirogonal prisms, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
359 Great tritrigonary cubaticubatidicubatidiapeiratic honeycomb Getit cacdicda Cubes, Ditrigonary triangular-hemiapeirogonal tilings, Small squarisquariapeirogonal tilings, Truncated cubes, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
360 Tritrigonary cubatitricubatiapeiratic honeycomb Totactica Triangular tilings, Great cubicuboctahedra, Small cubicuboctahedra, Great rhombicuboctahedra, Quasitruncated cuboctahedra Stut cadoca S4
361 Small tritrigonary dicubaticubatidiapeiratic honeycomb Stut dicacda Ditrigonary triangular-hemiapeirogonal tilings, Small squarisquariapeirogonal tilings, Small rhombicuboctahedra, Great rhombicuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4
362 Great tritrigonary dicubaticubatidiapeiratic honeycomb Getit dicacda Ditrigonary triangular-hemiapeirogonal tilings, Quasirhombicuboctahedra, Great squarisquariapeirogonal tilings, Quasitruncated cuboctahedra, Cuboctatruncated cuboctahedra Stut cadoca S4

Category 12: Prismatic Honeycombs[edit | edit source]

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry

Category 13: Prisms[edit | edit source]

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
Square tiling prism x4o4o2x () Square pyramid Cubes
2 square tilings
R3×A1
Truncated square tiling prism x4x4o2x () Sphenoid Cubes
Octagonal prisms
2 truncated square tilings
R3×A1
Snub square tiling prism s4s4s2x () Irregular pentagonal pyramid Cubes
Triangular prisms
2 snub square tilings
R3+×A1
Hexagonal tiling prism x6o3o2x () Triangular pyramid Hexagonal prisms
2 hexagonal tilings
V3×A1
Triangular tiling prism o6o3x2x () Hexagonal pyramid Triangular prisms
2 triangular tilings
V3×A1
Trihexagonal tiling prism o6x3o2x () Rectangular pyramid Triangular prisms
Hexagonal prisms
2 trihexagonal tilings
V3×A1
Truncated hexagonal tiling prism x6x3o2x () Sphenoid Triangular prisms
Dodecagonal prisms
2 truncated hexagonal tilings
V3×A1
Small rhombitrihexagonal tiling prism x6o3x2x () Isosceles trapezoidal pyramid Triangular prisms
Cubes
Hexagonal prisms
2 rhombitrihexagonal tilings
V3×A1
Great rhombitrihexagonal tiling prism x6x3x2x () Irregular tetrahedron Cubes
Hexagonal prisms
Dodecagonal prisms
2 great rhombitrihexagonal tilings
V3×A1
Snub trihexagonal tiling prism s6s3s2x () Irregular pentagonal pyramid Triangular prisms
Hexagonal prisms
2 snub trihexagonal tilings
V3+×A1
Elongated triangular tiling prism Irregular pentagonal pyramid Triangular prisms
Cubes
2 elongated triangular tilings
(W2❘W2+)×A1

Category 14: Other Slabs[edit | edit source]

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
Apeirogonal antiprism pseudoprismatic honeycomb Squathap xØo2s2s∞o () Hexagonal bipyramid cut in half perpendicularly to equator Triangular prisms
2 square tilings
Squathap
Triangular tiling antiprism Tratap o3o6s2s () Triangular cupola Tetrahedra
Octahedra
2 triangular tilings
Tratap

Category 15: Gyrates and Elongates[edit | edit source]

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry

Category 16: Miscellaneous Blends[edit | edit source]

This category contains blended honeycombs that don't fit into other categories and form small regiments.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry

Category 17: Skivcadach - Quiprich blends[edit | edit source]

This is a kaleidoscopic non-Wythoffian regiment formed by blending skivcadach from category 9 with quiprich from category 6. It contains 173 members.

Index Name OBSA Image Coxeter diagram Vertex figure Cells Symmetry

Category 18: Miscellaneous[edit | edit source]

Index Name OBSA Image Coxeter diagram Vertex figure Cells Regiment Symmetry
Antiprismatosnubretrosnub honeycomb Apsirsh Partial faceting of dodecadodecahedron Apeirogonal antiprisms
Icosahedra
Great icosahedra
Apsirsh

External links[edit | edit source]