List of uniform polytera

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Category A: Polychoric Prisms (2116 members)[edit | edit source]

Category B: Polygonal-Polyhedral Duoprisms (infinite)[edit | edit source]

Category C: Polygonal-Antiprismatic Duoprisms (infinite)[edit | edit source]

Category D: Duoprismatic Prisms (infinite)[edit | edit source]

Category E: Duoprismatic Spinoalterprisms (infinite)[edit | edit source]

Category 1: Primaries (#1-12)[edit | edit source]

These are the 3 flag-transitive polytera and their facetings, as well as the hin (demipenteract) regiment, which has a rectified pentachoron vertex figure and contains 6 members.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
1 Hexateron Hix Pentachoron 6 pen Hix
6 vertices 		Hix
15 edges 		Hix A5
2 Penteract Pent Pentachoron 10 tes Pent
32 vertices 		Pent
80 edges 		Pent B5
3 Triacontaditeron Tac Hexadecachoron 32 pen Tac
10 vertices 		Tac
40 edges 		Tac B5
4 Hexadecahemidecateron Hehad /2 Tesseractihemioctachoron 16 pen
5 hex 		Tac Tac Tac D5
5 Pentachoric hemiantiprism Phap 2+10 pen
5 tho 		Tac Tac Tac A4x2xA1+
6 Spinopentachoric hemiantiprism Nophap 20 pen
5 tho 		Tac Tac Tac A4x2xA1+
7 Demipenteract Hin Rectified pentachoron 10 hex
16 pen 		Hin
16 vertices 		Hin
80 edges 		Hin D5
8 Dishexadecateron Dah /2 Facetorectified pentachoron 16 pen
16 rap 		Hin Hin Hin D5
9 Hexadecapenteract Han Prismatointercepted pentachoron 10 hex
16 rap 		Hin Hin Hin D5
10 Retrodishexadecateron Radah 16 pen
16 firp 		Hin Hin Radah D5
11 Retropenteractihexadecateron Rinah 10 hex
16 firp 		Hin Hin Radah D5
12 Hexadecateron Hit Noble faceting of rectified pentachoron 16 pinnip Hin Hin Radah D5

Category 2: Truncates (#13-24)[edit | edit source]

These are the truncations, quasitruncations and bitruncations of the primaries, as well as their facetings. Their vertex figures are pyramids of the original edge figures (truncates) or scalenes of the original face figures.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
13 Truncated hexateron Tix Tetrahedral pyramid 6 pen
6 tip 		Tix
30 vertices 		Tix
75 edges 		Tix A5
14 Truncated penteract Tan Tetrahedral pyramid 10 tat
32 pen 		Tan
160 vertices 		Tan
400 edges 		Tan B5
15 Truncated triacontaditeron Tot Octahedral pyramid 32 tip
10 hex 		Tot
80 vertices 		Tot
280 edges 		Tot B5
16 Truncated hexadecahemidecateron Thehid /2 Tetrahemihexahedral pyramid 16 tip
5 thex
10 tho 		Tot Tot Tot D5
17 Quasitruncated penteract Quittin Tetrahedral pyramid 10 quitit
32 pen 		Scant
160 vertices 		Quittin
400 edges 		Quittin B5
18 Truncated demipenteract Thin Triangular prismatic pyramid 10 thex
16 tip
16 rap 		Thin
160 vertices 		Thin
560 edges 		Thin D5
19 Truncated dishexadecateron Tadah /2 Triangular retroprismatic pyramid 16 tip
16 grip
16 firp 		Thin Thin Tadah D5
20 Truncated hexadecapenteract Tohan Triangular toroprismatic pyramid 10 thex
16 grip
16 pinnip 		Thin Thin Tohan D5
21 Bitruncated hexateron Bittix Triangular scalene 6 deca
6 tip 		Bittix
60 vertices 		Bittix
150 edges 		Bittix A5
22 Bitruncated penteract Bittin Triangular scalene 10 tah
32 tip 		Bittin
320 vertices 		Bittin
800 edges 		Bittin B5
23 Bitruncated triacontaditeron Bittit Square scalene 32 deca
10 thex 		Bittit
240 vertices 		Bittit
720 edges 		Bittit B5
24 Bitruncated hexadecahemidecateron Bathehad /2 Bowtie scalene 16 deca
10 titho
5 tah 		Bittit Bittit Bathehad D5

Category 3: Rectates (#25-47)[edit | edit source]

These are the rectifications and birectifications of the primaries, with the exception of the larger regiments such as rat and nit. Rix (rectified hexateron) has 7 members, dot (dodecateron) has 5, and rin (rectified penteract) has 11. Their vertex figures are facetings of tetrahedral prisms (rix and rin) or the triangular duoprism (dot).

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
25 Rectified hexateron Rix Tetrahedral prism 6 rap
6 pen 		Rix
15 vertices 		Rix
60 edges 		A5
26 Cellibiprismatointercepted hexateron Cabnix Tetrahedral toroprism 6 rap
15 tepe
10 triddip 		Rix Rix A5
27 Facetorectified hexateron Firx /2 Tetrahedral retroprism 6 pen
15 tepe
10 triddip 		Rix Rix A5
28 Cellihexateron Cax 6 firp
15 tepe 		Rix Rix A5
29 Biprismatodishexateron Baddix 6 firp
6 pen
10 triddip 		Rix Rix A5
30 Cellintercepted dishexateron Cindax 6 pinnip
6 pen
15 tepe 		Rix Rix A5
31 Spinobiprismatohexateron Nobax 6 pinnip
10 triddip 		Rix Rix A5
32 Dodecateron Dot Triangular duoprism 12 rap Dot
20 vertices 		Dot
90 edges 		A5x2
33 Biprismatododecateron Bad 12 firp
20 triddip 		Dot Dot A5x2
34 Biprismatointercepted dodecateron Bend 12 pinnip
20 triddip 		Dot Dot A5x2
35 Cellibiprismatohexateron Cabbix 6 rap
15 ope
20 triddip 		Dot Dot A5
36 Cellidishexateron Caddix 6 firp
6 pinnip
15 ope 		Dot Dot A5
37 Rectified penteract Rin Tetrahedral prism 10 rit
32 pen 		Rin
80 vertices 		Rin
320 edges 		B5
38 Penteractitriacontadihemitriacontaditeron Nithit Tetrahedral toroprism 10 rit
32 tip
16 deca 		Rin Rin B5
39 Facetorectified penteract Firn Tetrahedral retroprism 32 pen
32 tip
16 deca 		Rin Rin B5
40 Triacontadipenteract Tin 10 firt
32 tip 		Rin Rin B5
41 Triacontadipenteractihemitriacontaditeron Tinhat 10 firt
32 pen
16 deca 		Rin Rin B5
42 Penteractidistriacontaditeron Niddit 10 hinnit
32 pen
32 tip 		Rin Rin B5
43 Penteractihemitriacontaditeron Noht 10 hinnit
16 deca 		Rin Rin B5
44 Penteractitriacontadihexadecateron Nath 10 sto
32 pen
16 tip 		Rin Rin D5
45 Penteractidishexadecateron Nadoh 10 sto
16 deca
16 tip 		Rin Rin D5
46 Penteractihexadecateron Nah 10 gotto
16 tip 		Rin Rin D5
47 Penteractitriacontadidishexadecateron Natdoh 10 gotto
32 pen
16 tip
16 deca 		Rin Rin D5

Category 4: Rat Regiment (#48-91)[edit | edit source]

Rat is the rectified triacontaditeron. Its vertex figure is the octahedral prism. There are 44 members.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
48 Rectified triacontaditeron Rat Octahedral prism 10 hex
32 rap 		Rat
40 vertices 		Rat
240 edges 		B5
49 Triacontadihemitriacontaditeron Thit 32 rap
16 duhd 		Rat Rat B5
50 Retrotriacontadihemitriacontaditeron Rithit 32 firp
16 spid 		Rat Rat B5
51 Octary penteractitriacontadihemitriacontaditeron Onthet 32 firp
10 hex
16 phud 		Rat Rat B5
52 Octary triacontadipenteractihemitriacontaditeron Otnahit 32 pinnip
10 hex
16 spid 		Rat Rat B5
53 Invertitriacontadihemitriacontaditeron Ithit 32 pinnip
16 phud 		Rat Rat B5
54 Retropenteractihemitriacontaditeron Rinhit /2 Crossed octahedral prism 10 hex
16 duhd 		Rat Rat B5
55 Cellitriacontadihemitriacontaditeron Cathit 32 rap
16 spid
40 ope 		Rat Rat B5
56 Biprismatotriacontadihemitriacontaditeron Bathit 32 rap
16 spid
80 tisdip 		Rat Rat B5
57 Cellipenteractitriacontaditeron Cant 10 hex
32 firp
40 ope 		Rat Rat B5
58 Biprismatopenteractitriacontaditeron Bant 10 hex
32 firp
80 tisdip 		Rat Rat B5
59 Retrotriacontadicellihemitriacontaditeron Ratchet 32 firp
16 duhd
40 ope 		Rat Rat B5
60 Retrotriacontadibiprismatohemitriacontaditeron Ratobaht 32 firp
16 duhd
80 tisdip 		Rat Rat B5
61 Cellitriacontaditeron Cat 32 pinnip
40 ope 		Rat Rat B5
62 Biprismatotriacontaditeron Bat 32 pinnip
80 tisdip 		Rat Rat B5
63 Cellipenteractihemitriacontaditeron Conhit 10 hex
16 spid
40 ope 		Rat Rat B5
64 Biprismatopenteractihemitriacontaditeron Bonhit 10 hex
16 spid
80 tisdip 		Rat Rat B5
65 Cellhemitriacontaditeron Chet 16 phud
40 ope 		Rat Rat B5
66 Biprismatohemitriacontaditeron Boht 16 phud
80 tisdip 		Rat Rat B5
67 Rectified hexadecahemidecateron Rhohid /2 Tetrahemihexahedral prism 10 tho
5 ico
16 rap 		Rat Rat D5
68 Biprismatopenteractidishexadecahemidecateron Bendhehad 10 tho
5 ico
16 firp
16 pinnip
80 tisdip 		Rat Rat D5
69 Penteractibiprismatodishexadecahemidecateron Nabadhehad 10 tho
5 ico
16 rap
16 spid
80 tisdip 		Rat Rat D5
70 Penteractitrishexadecahemidecateron Nathehid 10 tho
5 ico
16 firp
16 pinnip
16 spid 		Rat Rat D5
71 Penteractidishexadecahemidecateron Nedhehad 10 tho
5 ico
16 rap
16 duhd 		Rat Rat D5
72 Biprismatopenteractitrishexadecahemidecateron Benthahid 10 tho
5 ico
16 firp
16 pinnip
16 duhd
80 tisdip 		Rat Rat D5
73 Trishexadecapenteractihemidecateron Thinhed 10 tho
5 ico
16 firp
16 pinnip
16 phud 		Rat Rat D5
74 Hexadecapenteractihexadecahemidecateron Hinhohid 10 tho
5 ico
16 pinnip
16 piphid 		Rat Rat D5
75 Dishexadecabiprismatopenteractihemidecateron Dohbinhed 10 tho
5 ico
16 pinnip
16 piphid
80 tisdip 		Rat Rat D5
76 Penteractibiprismatotrishexadecahemidecateron Nabthehid 10 tho
5 ico
16 rap
16 firp
16 piphid
80 tisdip 		Rat Rat D5
77 Decadishexadecahemidecateron Didhehad 10 tho
5 ico
16 pinnip
16 nipdip 		Rat Rat D5
78 Penteractidishexadecabiprismatohemidecateron Nadahobhid 10 tho
5 ico
16 pinnip
16 nipdip
80 tisdip 		Rat Rat D5
79 Decatrishexadecahemidecateron Dathehid 10 tho
5 ico
16 rap
16 firp
16 nipdip 		Rat Rat D5
80 Hexadecahexadecateron Hah 16 firp
16 piphid 		Rat Rat D5
81 Penteractitrishexadecateron Noth 10 hex
16 rap
16 pinnip
16 piphid 		Rat Rat D5
82 Hexadecapenteractihexadecateron Hanoh 10 hex
16 firp
16 nipdip 		Rat Rat D5
83 Trishexadecateron Tuh 16 rap
16 pinnip
16 nipdip 		Rat Rat D5
84 Cellipenteractidishexadecateron Candoh 10 hex
16 firp
16 piphid
40 ope 		Rat Rat D5
85 Biprismatopenteractidishexadecateron Bandoh 10 hex
16 firp
16 piphid
80 tisdip 		Rat Rat D5
86 Cellitrishexadecateron Cath 16 rap
16 pinnip
16 piphid
40 ope 		Rat Rat D5
87 Biprismatotrishexadecateron Bath 16 rap
16 pinnip
16 piphid
80 tisdip 		Rat Rat D5
88 Cellidishexadecateron Cadoh 16 firp
16 nipdip
40 ope 		Rat Rat D5
89 Biprismatodishexadecateron Badoh 16 firp
16 nipdip
80 tisdip 		Rat Rat D5
90 Cellipenteractitrishexadecateron Canth 10 hex
16 rap
16 pinnip
16 nipdip
40 ope 		Rat Rat D5
91 Biprismatopenteractitrishexadecateron Banth 10 hex
16 rap
16 pinnip
16 nipdip
80 tisdip 		Rat Rat D5

Category 5: Nit Regiment (#92-240)[edit | edit source]

Nit is the penteractitriacontaditeron, which has a triangular-square duoprism vertex figure. It is the largest typical regiment among the nonprismatic uniform polytera, for it has 149 members.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
92 Penteractitriacontaditeron Nit Triangular-square duoprism 10 ico
32 rap 		Nit
80 vertices 		Nit
480 edges 		B5
93 Penteractitriacontadiretrotriacontaditeron Natrit 10 ico
32 firp
32 srip 		Nit Nit B5
94 Triacontadipenteractiretrotriacontaditeron Tinrit 10 ico
32 firp
32 pinnipdip 		Nit Nit B5
95 Penteractitriacontadinvertitriacontaditeron Notite 10 ico
32 pinnip
32 sirdop 		Nit Nit B5
96 Triacontadipenteractinvertitriacontaditeron Tonite 10 ico
32 pinnip
32 pirpop 		Nit Nit B5
97 Penteractiretrotriacontaditeron Nort 10 ico
32 rawvtip 		Nit Nit B5
98 Penteractinvertitriacontaditeron Nite 10 ico
32 pippindip 		Nit Nit B5
99 Biprismatotristesseractidistriacontaditeron Batatadit 10 gico
32 rap
32 srip
80 tisdip 		Nit Nit B5
100 Tristesseractibiprismatodistriacontaditeron Tatabadit 10 gico
32 rap
32 pinnipdip
80 tisdip 		Nit Nit B5
101 Biprismatotristesseractitriacontaditeron Batatat 10 gico
32 firp
80 tisdip 		Nit Nit B5
102 Invertibiprismatotristesseractidistriacontaditeron Ibtitdit 10 gico
32 pinnip
32 rawvtip
80 tisdip 		Nit Nit B5
103 Biprismatotristesseractilepidotriacontaditeron Batatilt 10 gico
32 sirdop
80 tisdip 		Nit Nit B5
104 Tristesseractibiprismatotriacontaditeron Titbit 10 gico
32 pirpop
80 tisdip 		Nit Nit B5
105 Biprismatocellitristesseractidistriacontaditeron Bactatdit 10 gico
32 rap
32 srip
40 ohope
40 shiddip 		Nit Nit B5
106 Biprismatocellitristesseractitriacontaditeron Bactatat 10 gico
32 firp
40 ohope
40 shiddip 		Nit Nit B5
107 Triacontadiretrotriacontaditeron Tart 32 rap
32 rawvtip 		Nit Nit B5
108 Triacontadinvertitriacontaditeron Tite 32 rap
32 pippindip 		Nit Nit B5
109 Retrolepidodistriacontaditeron Rildit 32 firp
32 sirdop 		Nit Nit B5
110 Retrofacetodistriacontaditeron Rifdit 32 firp
32 pirpop 		Nit Nit B5
111 Invertidistriacontaditeron Idit 32 pinnip
32 srip 		Nit Nit B5
112 Invertithyridodistriacontaditeron Iyidit 32 pinnip
32 pinnipdip 		Nit Nit B5
113 Spinotriacontaditeron Nat 32 garpop Nit Nit B5
114 Cellibiprismatoteron Cab 40 cope
80 tisdip 		Nit Nit B5
115 Lepidocellibiprismatoteron Locab 40 chope
40 shiddip 		Nit Nit B5

Category 6: Sphenoverts (#241-377)[edit | edit source]

These are all of the polytera with wedge vertex figures, which includes the cantellated polytera. There are 3 regiments with 15 members each, and 1 regiment with 92.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
241 Small rhombated hexateron Sarx Triangular prismatic wedge 6 srip
6 rap
15 tepe 		Sarx
60 vertices 		Sarx
240 edges 		A5
242 Retrosphenoverted hexateron Rawx Crossed triangular prismatic wedge 6 rawvtip
6 rap
6 tip 		Sarx Sarx A5
243 Lepidosphenoverted hexateron Lawx 6 sirdop
6 tip
15 tepe 		Sarx Sarx A5
244 Facetosphenoverted hexateron Fawx 6 tip
15 tepe
15 tuttip
20 thiddip 		Sarx Sarx A5
245 Lepidobiprismatosphenoverted hexateron Lawbix 6 sirdop
15 tuttip
20 thiddip 		Sarx Sarx A5
246 Sphenoverted hexateron Wax 6 srip
6 rap
6 tip
15 tuttip
20 thiddip 		Sarx Sarx A5
247 Retrosphenoverted cellihexateron Rawcax 6 rawvtip
6 rap
15 tepe
15 tuttip
20 thiddip 		Sarx Sarx A5
248 Quasisphenoverted cellihexateron Qwacox 6 pirpop
6 firp
15 tepe
15 tuttip 		Sarx Sarx A5
249 Quasisphenoverted biprismatohexateron Qwabix 6 pirpop
6 firp
6 tip
20 thiddip 		Sarx Sarx A5
250 Spinosphenoverted biprismatohexateron Nawbix 6 garpop
6 firp
15 tepe
20 thiddip 		Sarx Sarx A5
251 Spinosphenoverted cellihexateron Newcax 6 garpop
6 firp
6 tip
15 tuttip 		Sarx Sarx A5
252 Invertisphenoverted hexateron Iwax 6 pippindip
6 pinnip
15 tuttip 		Sarx Sarx A5
253 Invertisphenoverted biprismatohexateron Iwebix 6 pippindip
6 pinnip
6 tip
15 tepe
20 thiddip 		Sarx Sarx A5
254 Thyridosphenoverted hexateron Yawx 6 pinnipdip
6 pinnip
20 thiddip 		Sarx Sarx A5
255 Thyridosphenoverted cellihexateron Yawcax 6 pinnipdip
6 pinnip
6 tip
15 tepe
15 tuttip 		Sarx Sarx A5
256 Small rhombated penteract Sirn Triangular prismatic wedge 10 srit
32 rap
80 tepe 		Sirn
320 vertices 		Sirn
1280 edges 		B5
257 Retrosphenoverted penteract Rawn Crossed triangular prismatic wedge 10 rawvatoth
10 tat
32 rap 		Sirn Sirn B5
258 Small lepidosphenoverted penteract Slawn 10 sirdo
10 tat
80 tepe 		Sirn Sirn B5
259 Small facetosphenoverted penteract Safwan 10 tat
40 ticcup
80 tepe
80 todip 		Sirn Sirn B5
260 Small lepidosphenoverted biprismatopenteract Slawbin 10 sirdo
40 ticcup
80 todip 		Sirn Sirn B5
261 Sphenoverted penteract Wan 10 srit
32 rap
10 tat
40 ticcup
80 todip 		Sirn Sirn B5
262 Retrosphenoverted cellipenteract Rawcan 10 rawvatoth
32 rap
40 ticcup
80 tepe
80 todip 		Sirn Sirn B5
263 Small quasisphenoverted cellipenteract Sqwacon 10 spript
32 firp
40 ticcup
80 tepe 		Sirn Sirn B5
264 Small quasisphenoverted biprismatopenteract Sqwabin 10 spript
32 firp
10 tat
80 todip 		Sirn Sirn B5
265 Small spinosphenoverted biprismatopenteract Snawbin 10 garpit
32 firp
80 tepe
80 todip 		Sirn Sirn B5
266 Small spinosphenoverted cellipenteract Snowcan 10 garpit
32 firp
10 tat
40 ticcup 		Sirn Sirn B5
267 Invertisphenoverted penteract Iwan 10 pattinoth
32 pinnip
40 ticcup 		Sirn Sirn B5
268 Invertisphenoverted biprismatopenteract Iwebin 10 pattinoth
32 pinnip
10 tat
80 tepe
80 todip 		Sirn Sirn B5
269 Thyridosphenoverted penteract Yawn 10 pinpith
32 pinnip
80 todip 		Sirn Sirn B5
270 Thyridosphenoverted cellipenteract Yawcan 10 pinpith
32 pinnip
10 tat
40 ticcup
80 tepe 		Sirn Sirn B5
271 Sphenoverted penteractipenteractitriacontaditeron Wavinant Triangular prismatic wedge 10 wavitoth
10 quitit
32 rap 		Span
320 vertices 		Wavinant
1280 edges 		B5
272 Quasirhombated penteract Quarn Crossed triangular prismatic wedge 10 qrit
32 rap
80 tepe 		Span Wavinant B5
273 Great lepidosphenoverted penteract Glawn 10 girdo
10 quitit
80 tepe 		Span Wavinant B5
274 Great facetosphenoverted penteract Gafwan 10 quitit
40 quithip
80 tepe
80 tistodip 		Span Wavinant B5
275 Great lepidosphenoverted biprismatopenteract Glawbin 10 girdo
40 quithip
80 tistodip 		Span Wavinant B5
276 Sphenoverted cellipenteract Wacan 10 wavitoth
32 rap
40 quithip
80 tepe
80 tistodip 		Span Wavinant B5
277 Great retrosphenoverted penteract Grown 10 qrit
10 quitit
32 rap
40 quithip
80 tistodip 		Span Wavinant B5
278 Great quasisphenoverted biprismatopenteract Gaqwabin 10 gapript
10 quitit
32 firp
80 tistodip 		Span Wavinant B5
279 Great quasisphenoverted cellipenteract Gaqwacon 10 gapript
32 firp
40 quithip
80 tepe 		Span Wavinant B5
280 Great spinosphenoverted cellipenteract Gnowcan 10 gaqript
10 quitit
32 firp
40 quithip 		Span Wavinant B5
281 Great spinosphenoverted biprismatopenteract Gnawbin 10 gaqript
32 firp
80 tepe
80 tistodip 		Span Wavinant B5
282 Invertigreatosphenoverted penteract Igwan 10 dippanoth
32 pinnip
80 tistodip 		Span Wavinant B5
283 Invertisphenoverted cellipenteract Iwecan 10 dippanoth
10 quitit
32 pinnip
40 quithip
80 tepe 		Span Wavinant B5
284 Thyridogreatosphenoverted penteract Yagwan 10 pinnatoth
32 pinnip
40 quithip 		Span Wavinant B5
285 Thyridosphenoverted biprismatopenteract Yawbin 10 pinnatoth
10 quitit
32 pinnip
80 tepe
80 tistodip 		Span Wavinant B5
286 Small rhombated triacontaditeron Sart Cubic wedge 10 ico
32 srip
40 ope 		Sart
240 vertices 		Sart
1200 edges 		B5

Category 7: Birhombates (#378-447)[edit | edit source]

These are the bicantellated polytera which have duowedge vertex figures. Sibrid (small birhombidodecateron) has 23 members, while sibrant (small birhombipenteractitriacontaditeron) has 47 members.

Category 8: Fastegiumverts (#448-680)[edit | edit source]

These polytera have triangular fastegium or antifastegium vertex figures, including the runcinated polytera. There are 4 regiments with 37 members each, and 1 regiment with 85.

Category 9: Podiumverts (#681-721)[edit | edit source]

These are the expanded (stericated) polytera and all other polytera with podium vertex figures. There are 3 regiments, where 1 has 11 members and the other 2 have 15 members.

Category 10: Greater Truncates (#722-747)[edit | edit source]

This category includes the lone operative polytera other than the primaries and the truncates, with the exception of gart (great rhombated triacontaditeron) which has 2 members. Their vertex figures are irregular pentachora.

Category 11: Sphenopyriverts (#748-786)[edit | edit source]

These are the polytera with wedge pyramid vertex figures, which includes the runcitruncated polytera. There are 4 regiments with 7 members and 1 (pattit) with 11 members.

Category 12: Podipyriverts (#787-828)[edit | edit source]

These polytera have podium or antipodium pyramid vertex figures, including the steritruncated polytera. There are 6 regiments with 7 members each.

Category 13: Prismatorhombates and Kin (#829-870)[edit | edit source]

These polytera have trapezoid disphenoid or trapezoid pyramidal pyramid vertex figures. There are 14 regiments with 3 members each.

Category 14: Antisphenoverts (#871-942)[edit | edit source]

These are the stericantellated polytera, as well as polytera with related vertex figures. There are 3 regiments, where 1 has 18 members and the other 2 have 27 members.

Category 15: Siphin Regiment (#943-998)[edit | edit source]

Siphin (small prismatodemipenteract) has a tet || oct vertex figure. There are 56 members.

Category 16: Skivbadant and Gikvacadant Regiments (#999-1124)[edit | edit source]

These are the polytera with skewed duowedge vertex figures and their facetings. They have 63 members each.

Category 17: Sibacadint and Gidacadint Regiments (#1125-1154)[edit | edit source]

These are the polytera with skewed wedge pyramid vertex figures and their facetings. They have 15 members each.

Category 18: Skatbacadint Regiment (#1155-1287)[edit | edit source]

Skatbacadint (small skewtrigonary biprismatocellidis10-32teron) has a skewed antifastegium vertex figure. It is the second largest polyteron regiment, with 133 members.

Category 19: Miscellaneous (#1288-1297)[edit | edit source]

These are the atypical polytera that do not fit in any other category. This includes the two Johnson antiprisms, 6 in the hosiap regiment including itself, 2 with (F4/2×2×A1)/2 symmetry, and 3 with F4/2×A1 symmetry; and the sishia regiment which has 2 uniform members.

Index Name OBSA Picture Coxeter diagram Vertex figure Tera Army Regiment Company Symmetry
1288 Small ditetrahedronary hexacosihecatonicosachoric antiprism Sidtaxhiap Tetrahedron atop truncated tetrahedron 1200 pen
120 sidtidap
2 sidtaxhi 		Hipe
1200 vertices 		Sidtaxhiap
9600 edges 		Sidtaxhiap H4×A1
1289 Grand ditetrahedronary hexacosihecatonicosachoric antiprism Gadtaxhiap oo3oo3xo5ox3/2*b&#x Tetrahedron atop quasitruncated tetrahedron 1200 pen
120 gidtidap
2 gadtaxhi 		Hipe
1200 vertices 		Gadtaxhiap
9600 edges 		Gadtaxhiap H4×A1
1290 Hollow stellated icositetrachoric antiprism Hosiap 48 hex as 24 haddet
96 pen as 48 sopy 		Icope
48 vertices 		Hosiap
336 edges 		Hosiap F4×A1
1291 Inverted hollow stellated icositetrachoric antiprism Ihsiap 48 hex as 24 haddet
48 pen
48 rap 		Icope
48 vertices 		Hosiap
336 edges 		Hosiap (F4/2×2×A1)/2
1292 Hollow stellated icositetrachoric retroantiprism Hesirap 48 hex as 24 haddet
48 pen
48 firp 		Icope
48 vertices 		Hosiap
336 edges 		Hesirap (F4/2×2×A1)/2
1295 Retrohollow stellated icositetrachoric antiprism Rahsiap 48 pen
48 tepe
48 firp 		Icope
48 vertices 		Hosiap
336 edges 		Rahsiap F4/2×A1
1296 Spinohollow stellated icositetrachoric hemiantiprism Nahsihap 48 tho
48 rap
48 pen 		Icope
48 vertices 		Hosiap
336 edges 		Nahsihap F4/2×A1
1297 Hollow stellated icositetrachoric hemiantiprism Hesihap 96 pen
48 tepe
48 pinnip
48 tho 		Icope
48 vertices 		Hosiap
336 edges 		Hesihap F4/2×A1
1293 Dodecahedronary prismatohexacosichoric alterprism Dopixa 120 spid as 2 dopix
1200 firp
2400 tepe 		Exip
240 vertices 		Sishia
3840 edges 		H4×A1
1294 Invertidodecahedronary hecatonicosachoric alterprism Idhia 2 idhi
120 ditdidap
720 pappip
1440 trapedip 		Exip
240 vertices 		Sishia
3840 edges 		H4×A1
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