List of noble polychora

Pentachoric symmetry

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

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

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

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

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