List of noble polychora

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Pentachoric symmetry[edit | edit source]

Hull ID Name Cells Cell Vertex figure Fissary
Pentachoron
5 vertices
1 Pentachoron 5
Rectified pentachoron
10 vertices
2 Noble faceting of rectified pentachoron 10 Triangular toroprism (pinnip verf)

Decachoric symmetry[edit | edit source]

Hull ID Name Cells Cell Vertex figure Fissary
Bidecachoron
10 vertices
3a Bidecachoron 30 Tetragonal disphenoid Triakis tetrahedron
Small prismatodecachoron
20 vertices
1a Noble faceting of small prismatodecachoron 1 60 Crossed butterfly wedge (garpop verf)
2a Noble faceting of small prismatodecachoron 2 120 Bowtie pyramid (ripdip verf) Yes
Biambodecachoron
20 vertices
7a Noble faceting of biambodecachoron 1 40 Faceting of triangular prism
8a Noble faceting of biambodecachoron 2 60 Windowed wedge Yes
9a Noble faceting of biambodecachoron 3 60 Wedge
10a Noble faceting of biambodecachoron 4 60 Crossed butterfly wedge
11a Noble faceting of biambodecachoron 5 120 Skewed bowtie pyramid
12a Noble faceting of biambodecachoron 6 120 Phyllic disphenoid
Decachoron
30 vertices
3b Decachoron 10 Truncated tetrahedron
4a Noble faceting of decachoron 40 Faceting of triangular cupola
Bitruncatodecachoron
40 vertices
7b 20
4b 30 Yes
5 40
6 40
Small birhombatodecachoron
60 vertices
1b 20
Rectified small prismatodecachoron
60 vertices
8b 20
9b 20
10b 20
Small biprismatorhombatodecachoron
120 vertices
2b 20
Transitional bicantitruncatodecachoron
120 vertices
11b 20
Great prismatodecachoron
120 vertices
12b 20

Tesseractic symmetry[edit | edit source]

Hull ID Name Cells Cell Vertex figure Fissary
Hexadecachoron
8 vertices
1a Hexadecachoron 16
Tesseract
16 vertices
1b Tesseract 8
2a Noble faceting of tesseract 32 Triangular toroprism (ini verf)
Icositetrachoron
24 vertices
6a 64 Faceting of triangular prism (sto verf)
7a 96 Windowed wedge (hinpith verf)
8a 96 Butterfly wedge (sirth verf)
Rectified tesseract
32 vertices
2b Noble faceting of rectified tesseract 1 16 Faceting of truncated tetrahedron
3a Noble faceting of rectified tesseract 2 48 Faceting of square antipodium
4a Noble faceting of rectified tesseract 3 192 Rectangular pyramid Yes
5a Noble faceting of rectified tesseract 4 384 Irregular tetrahedron Yes
Truncated hexadecachoron
48 vertices
3b 32 Faceting of triangular orthobicupola
9a 64 Faceting of triangular cupola Yes
10a 64 Faceting of triangular cupola Yes
11a 64 Faceting of triangular cupola Yes
12a 64 Faceting of triangular cupola Yes
13a 64 Faceting of triangular cupola Yes
Truncated tesseract
64 vertices
12b 48 Faceting of square cupola
13b 48 Faceting of square cupola
Small disprismatotesseractihexadecachoron
64 vertices
6b 24 Faceting of square orthobicupola
9b 48 Faceting of square cupola
10b 48 Faceting of square cupola
11b 48 Faceting of square cupola
Small rhombated tesseract
96 vertices
15a 192 Faceting of elongated digonal cupola Yes
16a 192 Faceting of elongated digonal cupola Yes
Rectified icositetrachoron
96 vertices
7b 24 Faceting of rhombicuboctahedron
8b 24 Faceting of rhombicuboctahedron
14 96 Faceting of hexagonal prism
Truncated icositetrachoron
192 vertices
4b 32
15b 96 Faceting of elongated square cupola
16b 96 Faceting of elongated square cupola
Great disprismatotesseractihexadecachoron
384 vertices
5b 32

Icositetrachoric symmetry[edit | edit source]

Hull ID Name Cells Cell Vertex figure Fissary
Icositetrachoron
24 vertices
1 Icositetrachoron 24
2a 96 Triangular prism (rico verf) Great triakis octahedron
3a 96 Triangular retroprism (frico verf)
4a 96 Triangular prism (rit verf) Excavated cube
5a 96 Triangular retroprism (firt verf)
6a 96 Triangular toroprism (hinnit verf)
Rectified icositetrachoron
96 vertices
2b 24 Quasitruncated cube
3b 24 Faceting of rhombicuboctahedron
4b 24 Hypertruncated octahedron
5b 24 Faceting of truncated octahedron
6b 24 Faceting of truncated octahedron
7a 144 Faceting of square cupola
8a 144 Faceting of square cupola Yes
9a 192 Faceting of triangular cupola
10a 192 Faceting of triangular cupola
11a 192 Faceting of ditrigonal frustum
12a 192 Faceting of ditrigonal frustum
13a 192 Faceting of ditrigonal frustum Yes
14a 192 Faceting of ditrigonal frustum Yes
15a 576 Blend of 2 square pyramids (sobthex verf) Yes
Small prismatotetracontoctachoron
144 vertices
7b 96 Faceting of elongated triangular orthobicupola Yes
8b 96 Faceting of elongated triangular orthobicupola
16a 192 Faceting of elongated triangular cupola Yes
17a 192 Faceting of elongated triangular cupola Yes
18a 288 Faceting of irregular hexagonal prism Yes
19a 288 Faceting of irregular elongated hexagonal bipyramid Yes
20a 576 Yes
21a 576 Yes
22a 576 Yes
23a 576 Yes

Hecatonicosachoric symmetry[edit | edit source]

Hull ID Name Cells Cell Vertex figure Fissary
Hexacosichoron
120 vertices
1 Great hecatonicosachoron 120 Great dodecahedron Small stellated dodecahedron
2 Grand stellated hecatonicosachoron 120 Small stellated dodecahedron Great dodecahedron
3a Grand hecatonicosachoron 120 Dodecahedron Great icosahedron
3b Great stellated hecatonicosachoron 120 Great stellated dodecahedron Icosahedron
4a Faceted hexacosichoron 120 Icosahedron Great dodecahedron
4b Small stellated hecatonicosachoron 120 Small stellated dodecahedron Dodecahedron
5a Great faceted hexacosichoron 120 Great icosahedron Small stellated dodecahedron
5b Great grand hecatonicosachoron 120 Great dodecahedron Great stellated dodecahedron
6a Invertidodecahedronary hecatonicosachoron 120 Ditrigonary dodecadodecahedron Ditrigonal icosahedron
6b Ditrigonal hecatonicosachoron 120 Ditrigonal icosahedron Medial triambic icosahedron
7 120 Didhi verf
8 120 Ofiddady verf
9a 120 Sitpodady verf Yes
9b 120 Gitpodady verf Yes
10a Hexacosichoron 600 Tetrahedron Icosahedron
11a Grand hexacosichoron 600 Tetrahedron Great icosahedron
12a 600 Gardatady verf
13a 600 Gadtardy verf
14a 600 Gaid tathi verf
15a 600 Gardatathi verf
16a 600 Gadatady verf
17a 600 Gadtacady verf Yes
18a 600 Gadtachi verf Yes
19a 600 Gadtifady verf Yes
20a 600 Sirdatady verf
21a 600 Sridatady verf
22a 600 Sridtathi verf
23a 600 Sand tathi verf
24a 600 Siddatady verf
25a 600 Sidtacady verf Yes
26a 600 Siddatchi verf Yes
27a 600 Sadtifady verf Yes
? Small tripesic hecatonicosachoron 120 Truncated great dodecahedron Compound of 3 tetragonal disphenoids Yes
? Great tripesic hecatonicosachoron 120 Quasitruncated small stellated dodecahedron Compound of 3 tetragonal disphenoids Yes