List of uniform polyhedra by Wythoff symbol

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Polyhedron
Class Number and properties
Platonic solids
(5, convex, regular)
Archimedean solids
(13, convex, uniform)
Kepler–Poinsot polyhedra
(4, regular, non-convex)
Uniform polyhedra
(75, uniform)
Prismatoid:
prisms, antiprisms etc.
(4 infinite uniform classes)
Polyhedra tilings (11 regular, in the plane)
Quasi-regular polyhedra
(8)
Johnson solids (92, convex, non-uniform)
Pyramids and Bipyramids (infinite)
Stellations Stellations
Polyhedral compounds (5 regular)
Deltahedra (Deltahedra,
equilateral triangle faces)
Snub polyhedra
(12 uniform, not mirror image)
Zonohedron (Zonohedra,
faces have 180°symmetry)
Dual polyhedron
Self-dual polyhedron (infinite)
Catalan solid (13, Archimedean dual)

There are many relations among the uniform polyhedra.

Here they are grouped by the Wythoff symbol.

Key[edit]

Image
Name
Bowers pet name
V Number of vertices,E Number of edges,F Number of faces=Face configuration
?=Euler characteristic, group=Symmetry group
Wythoff symbol - Vertex figure
W - Wenninger number, U - Uniform number, K- Kaleido number, C -Coxeter number
alternative name
second alternative name

Regular[edit]

All the faces are identical, each edge is identical and each vertex is identical. They all have a Wythoff symbol of the form p|q 2.

Convex[edit]

The Platonic solids.

Tetrahedron.png
Tetrahedron
Tet
V 4,E 6,F 4=4{3}
χ=2, group=Td, A3, [3,3], (*332)
3 | 2 3
| 2 2 2 - 3.3.3
W1, U01, K06, C15

Octahedron (vector).svg
Octahedron
Oct
V 6,E 12,F 8=8{3}
χ=2, group=Oh, BC3, [4,3], (*432)
4 | 2 3 - 3.3.3.3
W2, U05, K10, C17

Hexahedron.png
Hexahedron
Cube
V 8,E 12,F 6=6{4}
χ=2, group=Oh, B3, [4,3], (*432)
3 | 2 4 - 4.4.4
W3, U06, K11, C18

Icosahedron.png
Icosahedron
Ike
V 12,E 30,F 20=20{3}
χ=2, group=Ih, H3, [5,3], (*532)
5 | 2 3 - 3.3.3.3.3
W4, U22, K27, C25

Dodecahedron.png
Dodecahedron
Doe
V 20,E 30,F 12=12{5}
χ=2, group=Ih, H3, [5,3], (*532)
3 | 2 5 - 5.5.5
W5, U23, K28, C26

Non-convex[edit]

The Kepler-Poinsot solids.

Great icosahedron.png
Great icosahedron
Gike
V 12,E 30,F 20=20{3}
χ=2, group=Ih, H3, [5,3], (*532)
5/2 | 2 3 - (35)/2
W41, U53, K58, C69

Great dodecahedron.png
Great dodecahedron
Gad
V 12,E 30,F 12=12{5}
χ=-6, group=Ih, H3, [5,3], (*532)
5/2 | 2 5 - (55)/2
W21, U35, K40, C44

Small stellated dodecahedron.png
Small stellated dodecahedron
Sissid
V 12,E 30,F 12=125
χ=-6, group=Ih, H3, [5,3], (*532)
5 | 25/2 - (5/2)5
W20, U34, K39, C43

Great stellated dodecahedron.png
Great stellated dodecahedron
Gissid
V 20,E 30,F 12=125
χ=2, group=Ih, H3, [5,3], (*532)
3 | 25/2 - (5/2)3
W22, U52, K57, C68

Quasi-regular[edit]

Each edge is identical and each vertex is identical. There are two types of faces which appear in an alternating fashion around each vertex. The first row are semi-regular with 4 faces around each vertex. They have Wythoff symbol 2|p q. The second row are ditrigonal with 6 faces around each vertex. They have Wythoff symbol 3|p q or 3/2|p q.

Polyhedron 6-8 max.png
Cuboctahedron
Co
V 12,E 24,F 14=8{3}+6{4}
χ=2, group=Oh, B3, [4,3], (*432), order 48
Td, [3,3], (*332), order 24
2 | 3 4
3 3 | 2 - 3.4.3.4
W11, U07, K12, C19

Polyhedron 12-20 max.png
Icosidodecahedron
Id
V 30,E 60,F 32=20{3}+12{5}
χ=2, group=Ih, H3, [5,3], (*532), order 120
2 | 3 5 - 3.5.3.5
W12, U24, K29, C28

Great icosidodecahedron.png
Great icosidodecahedron
Gid
V 30,E 60,F 32=20{3}+12{5/2}
χ=2, group=Ih, [5,3], *532
2 | 3 5/2
2 | 3 5/3
2 | 3/2 5/2
2 | 3/2 5/3 - 3.5/2.3.5/2
W94, U54, K59, C70

Dodecadodecahedron.png
Dodecadodecahedron
Did
V 30,E 60,F 24=12{5}+12{5/2}
χ=−6, group=Ih, [5,3], *532
2 | 5 5/2
2 | 5 5/3
2 | 5/2 5/4
2 | 5/3 5/4 - 5.5/2.5.5/2
W73, U36, K41, C45

Small ditrigonal icosidodecahedron.png
Small ditrigonal icosidodecahedron
Sidtid
V 20,E 60,F 32=20{3}+12{5/2}
χ=−8, group=Ih, [5,3], *532
3 | 5/2 3 - (3.5/2)3
W70, U30, K35, C39

Ditrigonal dodecadodecahedron.png
Ditrigonal dodecadodecahedron
Ditdid
V 20,E 60,F 24=12{5}+12{5/2}
χ=−16, group=Ih, [5,3], *532
3 | 5/3 5
3/2 | 5 5/2
3/2 | 5/3 5/4
3 | 5/2 5/4 - (5.5/3)3
W80, U41, K46, C53

Great ditrigonal icosidodecahedron.png
Great ditrigonal icosidodecahedron
Gidtid
V 20,E 60,F 32=20{3}+12{5}
χ=−8, group=Ih, [5,3], *532
3/2 | 3 5
3 | 3/2 5
3 | 3 5/4
3/2 | 3/2 5/4 - ((3.5)3)/2
W87, U47, K52, C61

Wythoff p q|r[edit]

Truncated regular forms[edit]

Each vertex has three faces surrounding it, two of which are identical. These all have Wythoff symbols 2 p|q, some are constructed by truncating the regular solids.

Polyhedron truncated 4a max.png
Truncated tetrahedron
Tut
V 12,E 18,F 8=4{3}+4{6}
χ=2, group=Td, A3, [3,3], (*332), order 24
2 3 | 3 - 3.6.6
W6, U02, K07, C16

Polyhedron truncated 8 max.png
Truncated octahedron
Toe
V 24,E 36,F 14=6{4}+8{6}
χ=2, group=Oh, B3, [4,3], (*432), order 48
Th, [3,3] and (*332), order 24
2 4 | 3
3 3 2 | - 4.6.6
W7, U08, K13, C20

Polyhedron truncated 6 max.png
Truncated cube
Tic
V 24,E 36,F 14=8{3}+6{8}
χ=2, group=Oh, B3, [4,3], (*432), order 48
2 3 | 4 - 3.8.8
W8, U09, K14, C21
Truncated hexahedron

Polyhedron truncated 20 max.png
Truncated icosahedron
Ti
V 60,E 90,F 32=12{5}+20{6}
χ=2, group=Ih, H3, [5,3], (*532), order 120
2 5 | 3 - 5.6.6
W9, U25, K30, C27

Polyhedron truncated 12 max.png
Truncated dodecahedron
Tid
V 60,E 90,F 32=20{3}+12{10}
χ=2, group=Ih, H3, [5,3], (*532), order 120
2 3 | 5 - 3.10.10
W10, U26, K31, C29

Great truncated dodecahedron.png
Truncated great dodecahedron
Tigid
V 60,E 90,F 24=12{5/2}+12{10}
χ=−6, group=Ih, [5,3], *532
2 5/2 | 5
2 5/3 | 5 - 10.10.5/2
W75, U37, K42, C47

Great truncated icosahedron.png
Truncated great icosahedron
Tiggy
V 60,E 90,F 32=12{5/2}+20{6}
χ=2, group=Ih, [5,3], *532
2 5/2 | 3
2 5/3 | 3 - 6.6.5/2
W95, U55, K60, C71

Stellated truncated hexahedron.png
Stellated truncated hexahedron
Quith
V 24,E 36,F 14=8{3}+6{8/3}
χ=2, group=Oh, [4,3], *432
2 3 | 4/3
2 3/2 | 4/3 - 3.8/3.8/3
W92, U19, K24, C66
Quasitruncated hexahedron stellatruncated cube

Small stellated truncated dodecahedron.png
Small stellated truncated dodecahedron
Quit Sissid
V 60,E 90,F 24=12{5}+12{10/3}
χ=−6, group=Ih, [5,3], *532
2 5 | 5/3
2 5/4 | 5/3 - 5.10/3.10/3
W97, U58, K63, C74
Quasitruncated small stellated dodecahedron Small stellatruncated dodecahedron

Great stellated truncated dodecahedron.png
Great stellated truncated dodecahedron
Quit Gissid
V 60,E 90,F 32=20{3}+12{10/3}
χ=2, group=Ih, [5,3], *532
2 3 | 5/3 - 3.10/3.10/3
W104, U66, K71, C83
Quasitruncated great stellated dodecahedron Great stellatruncated dodecahedron

Hemipolyhedra[edit]

The hemipolyhedra all have faces which pass through the origin. Their Wythoff symbols are of the form p p/m|q or p/m p/n|q. With the exception of the tetrahemihexahedron they occur in pairs, and are closely related to the semi-regular polyhedra, like the cuboctohedron.

Tetrahemihexahedron.png
Tetrahemihexahedron
Thah
V 6,E 12,F 7=4{3}+3{4}
χ=1, group=Td, [3,3], *332
3/2 3 | 2 (double-covering) - 3.4.3/2.4
W67, U04, K09, C36

Octahemioctahedron.png
Octahemioctahedron
Oho
V 12,E 24,F 12=8{3}+4{6}
χ=0, group=Oh, [4,3], *432
3/2 3 | 3 - 3.6.3/2.6
W68, U03, K08, C37

Cubohemioctahedron.png
Cubohemioctahedron
Cho
V 12,E 24,F 10=6{4}+4{6}
χ=−2, group=Oh, [4,3], *432
4/3 4 | 3 (double-covering) - 4.6.4/3.6
W78, U15, K20, C51

Small icosihemidodecahedron.png
Small icosihemidodecahedron
Seihid
V 30,E 60,F 26=20{3}+6{10}
χ=−4, group=Ih, [5,3], *532
3/2 3 | 5 (double covering) - 3.10.3/2.10
W89, U49, K54, C63

Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Sidhid
V 30,E 60,F 18=12{5}+6{10}
χ=−12, group=Ih, [5,3], *532
5/4 5 | 5 - 5.10.5/4.10
W91, U51, K56, C65

Great icosihemidodecahedron.png
Great icosihemidodecahedron
Geihid
V 30,E 60,F 26=20{3}+6{10/3}
χ=−4, group=Ih, [5,3], *532
3/2 3 | 5/3 - 3.10/3.3/2.10/3
W106, U71, K76, C85

Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Gidhid
V 30,E 60,F 18=12{5/2}+6{10/3}
χ=−12, group=Ih, [5,3], *532
5/3 5/2 | 5/3 (double covering) - 5/2.10/3.5/3.10/3
W107, U70, K75, C86

Great dodecahemicosahedron.png
Great dodecahemicosahedron
Gidhei
V 30,E 60,F 22=12{5}+10{6}
χ=−8, group=Ih, [5,3], *532
5/4 5 | 3 (double covering) - 5.6.5/4.6
W102, U65, K70, C81

Small dodecahemicosahedron.png
Small dodecahemicosahedron
Sidhei
V 30,E 60,F 22=12{5/2}+10{6}
χ=−8, group=Ih, [5,3], *532
5/3 5/2 | 3 (double covering) - 6.5/2.6.5/3
W100, U62, K67, C78

Rhombic quasi-regular[edit]

Four faces around the vertex in the pattern p.q.r.q. The name rhombic stems from inserting a square in the cuboctahedron and icosidodecahedron. The Wythoff symbol is of the form p q|r.

Polyhedron small rhombi 6-8 max.png

Rhombicuboctahedron
Sirco
V 24,E 48,F 26=8{3}+(6+12){4}
χ=2, group=Oh, B3, [4,3], (*432), order 48
3 4 | 2 - 3.4.4.4
W13, U10, K15, C22
Rhombicuboctahedron

Small cubicuboctahedron.png
Small cubicuboctahedron
Socco
V 24,E 48,F 20=8{3}+6{4}+6{8}
χ=−4, group=Oh, [4,3], *432
3/2 4 | 4
3 4/3 | 4 - 4.8.3/2.8
W69, U13, K18, C38

Great cubicuboctahedron.png
Great cubicuboctahedron
Gocco
V 24,E 48,F 20=8{3}+6{4}+6{8/3}
χ=−4, group=Oh, [4,3], *432
3 4 | 4/3
4 3/2 | 4 - 3.8/3.4.8/3
W77, U14, K19, C50

Uniform great rhombicuboctahedron.png
Nonconvex great rhombicuboctahedron
Querco
V 24,E 48,F 26=8{3}+(6+12){4}
χ=2, group=Oh, [4,3], *432
3/2 4 | 2
3 4/3 | 2 - 4.4.4.3/2
W85, U17, K22, C59
Quasirhombicuboctahedron

Polyhedron small rhombi 12-20 max.png

Rhombicosidodecahedron
Srid
V 60,E 120,F 62=20{3}+30{4}+12{5}
χ=2, group=Ih, H3, [5,3], (*532), order 120
3 5 | 2 - 3.4.5.4
W14, U27, K32, C30
Rhombicosidodecahedron

Small dodecicosidodecahedron.png
Small dodecicosidodecahedron
Saddid
V 60,E 120,F 44=20{3}+12{5}+12{10}
χ=−16, group=Ih, [5,3], *532
3/2 5 | 5
3 5/4 | 5 - 5.10.3/2.10
W72, U33, K38, C42

Great dodecicosidodecahedron.png
Great dodecicosidodecahedron
Gaddid
V 60,E 120,F 44=20{3}+12{5/2}+12{10/3}
χ=−16, group=Ih, [5,3], *532
5/2 3 | 5/3
5/3 3/2 | 5/3 - 3.10/3.5/2.10/7
W99, U61, K66, C77

Uniform great rhombicosidodecahedron.png
Nonconvex great rhombicosidodecahedron
Qrid
V 60,E 120,F 62=20{3}+30{4}+12{5/2}
χ=2, group=Ih, [5,3], *532
5/3 3 | 2
5/2 3/2 | 2 - 3.4.5/3.4
W105, U67, K72, C84
Quasirhombicosidodecahedron

Small icosicosidodecahedron.png
Small icosicosidodecahedron
Siid
V 60,E 120,F 52=20{3}+12{5/2}+20{6}
χ=−8, group=Ih, [5,3], *532
5/2 3 | 3 - 6.5/2.6.3
W71, U31, K36, C40

Small ditrigonal dodecicosidodecahedron.png
Small ditrigonal dodecicosidodecahedron
Sidditdid
V 60,E 120,F 44=20{3}+12{5/2}+12{10}
χ=−16, group=Ih, [5,3], *532
5/3 3 | 5
5/2 3/2 | 5 - 3.10.5/3.10
W82, U43, K48, C55

Rhombidodecadodecahedron.png
Rhombidodecadodecahedron
Raded
V 60,E 120,F 54=30{4}+12{5}+12{5/2}
χ=−6, group=Ih, [5,3], *532
5/2 5 | 2 - 4.5/2.4.5
W76, U38, K43, C48

Icosidodecadodecahedron.png
Icosidodecadodecahedron
Ided
V 60,E 120,F 44=12{5}+12{5/2}+20{6}
χ=−16, group=Ih, [5,3], *532
5/3 5 | 3
5/2 5/4 | 3 - 5.6.5/3.6
W83, U44, K49, C56

Great ditrigonal dodecicosidodecahedron.png
Great ditrigonal dodecicosidodecahedron
Gidditdid
V 60,E 120,F 44=20{3}+12{5}+12{10/3}
χ=−16, group=Ih, [5,3], *532
3 5 | 5/3
5/4 3/2 | 5/3 - 3.10/3.5.10/3
W81, U42, K47, C54

Great icosicosidodecahedron.png
Great icosicosidodecahedron
Giid
V 60,E 120,F 52=20{3}+12{5}+20{6}
χ=−8, group=Ih, [5,3], *532
3/2 5 | 3
3 5/4 | 3 - 5.6.3/2.6
W88, U48, K53, C62

Even-sided forms[edit]

Wythoff p q r|[edit]

These have three different faces around each vertex, and the vertices do not lie on any plane of symmetry. They have Wythoff symbol p q r|, and vertex figures 2p.2q.2r.

Polyhedron great rhombi 6-8 max.png
Truncated cuboctahedron
Girco
V 48,E 72,F 26=12{4}+8{6}+6{8}
χ=2, group=Oh, B3, [4,3], (*432), order 48
2 3 4 | - 4.6.8
W15, U11, K16, C23
Rhombitruncated cuboctahedron Truncated cuboctahedron

Great truncated cuboctahedron.png
Great truncated cuboctahedron
Quitco
V 48,E 72,F 26=12{4}+8{6}+6{8/3}
χ=2, group=Oh, [4,3], *432
2 3 4/3 | - 4.6/5.8/3
W93, U20, K25, C67
Quasitruncated cuboctahedron

Cubitruncated cuboctahedron.png
Cubitruncated cuboctahedron
Cotco
V 48,E 72,F 20=8{6}+6{8}+6{8/3}
χ=−4, group=Oh, [4,3], *432
3 4 4/3 | - 6.8.8/3
W79, U16, K21, C52
Cuboctatruncated cuboctahedron

Polyhedron great rhombi 12-20 max.png
Truncated icosidodecahedron
Grid
V 120,E 180,F 62=30{4}+20{6}+12{10}
χ=2, group=Ih, H3, [5,3], (*532), order 120
2 3 5 | - 4.6.10
W16, U28, K33, C31
Rhombitruncated icosidodecahedron Truncated icosidodecahedron

Great truncated icosidodecahedron.png
Great truncated icosidodecahedron
Gaquatid
V 120,E 180,F 62=30{4}+20{6}+12{10/3}
χ=2, group=Ih, [5,3], *532
2 3 5/3 | - 4.6.10/3
W108, U68, K73, C87
Great quasitruncated icosidodecahedron

Icositruncated dodecadodecahedron.png
Icositruncated dodecadodecahedron
Idtid
V 120,E 180,F 44=20{6}+12{10}+12{10/3}
χ=−16, group=Ih, [5,3], *532
3 5 5/3 | - 6.10.10/3
W84, U45, K50, C57
Icosidodecatruncated icosidodecahedron

Truncated dodecadodecahedron.png
Truncated dodecadodecahedron
Quitdid
V 120,E 180,F 54=30{4}+12{10}+12{10/3}
χ=−6, group=Ih, [5,3], *532
2 5 5/3 | - 4.10/9.10/3
W98, U59, K64, C75
Quasitruncated dodecahedron

Wythoff p q (r s)|[edit]

Vertex figure p.q.-p.-q. Wythoff p q (r s)|, mixing pqr| and pqs|.

Small rhombihexahedron.png
Small rhombihexahedron
Sroh
V 24,E 48,F 18=12{4}+6{8}
χ=−6, group=Oh, [4,3], *432
2 4 (3/2 4/2) | - 4.8.4/3.8
W86, U18, K23, C60

Great rhombihexahedron.png
Great rhombihexahedron
Groh
V 24,E 48,F 18=12{4}+6{8/3}
χ=−6, group=Oh, [4,3], *432
2 4/3 (3/2 4/2) | - 4.8/3.4/3.8/5
W103, U21, K26, C82

Rhombicosahedron.png
Rhombicosahedron
Ri
V 60,E 120,F 50=30{4}+20{6}
χ=−10, group=Ih, [5,3], *532
2 3 (5/4 5/2) | - 4.6.4/3.6/5
W96, U56, K61, C72

Great rhombidodecahedron.png
Great rhombidodecahedron
Gird
V 60,E 120,F 42=30{4}+12{10/3}
χ=−18, group=Ih, [5,3], *532
2 5/3 (3/2 5/4) | - 4.10/3.4/3.10/7
W109, U73, K78, C89

Great dodecicosahedron.png
Great dodecicosahedron
Giddy
V 60,E 120,F 32=20{6}+12{10/3}
χ=−28, group=Ih, [5,3], *532
3 5/3 (3/2 5/2) | - 6.10/3.6/5.10/7
W101, U63, K68, C79

Small rhombidodecahedron.png
Small rhombidodecahedron
Sird
V 60,E 120,F 42=30{4}+12{10}
χ=−18, group=Ih, [5,3], *532
2 5 (3/2 5/2) | - 4.10.4/3.10/9
W74, U39, K44, C46

Small dodecicosahedron.png
Small dodecicosahedron
Siddy
V 60,E 120,F 32=20{6}+12{10}
χ=−28, group=Ih, [5,3], *532
3 5 (3/2 5/4) | - 6.10.6/5.10/9
W90, U50, K55, C64

Snub polyhedra[edit]

These have Wythoff symbol |p q r, and one non-Wythoffian construction is given |p q r s.

Wythoff |p q r[edit]

Symmetry group
O

Polyhedron snub 6-8 left max.png
Snub cube
Snic
V 24,E 60,F 38=(8+24){3}+6{4}
χ=2, group=O, 1/2B3, [4,3]+, (432), order 24
| 2 3 4 - 3.3.3.3.4
W17, U12, K17, C24

Ih

Small snub icosicosidodecahedron.png
Small snub icosicosidodecahedron
Seside
V 60,E 180,F 112=(40+60){3}+12{5/2}
χ=−8, group=Ih, [5,3], *532
|5/2 3 3 - 35.5/2
W110, U32, K37, C41

Small retrosnub icosicosidodecahedron.png
Small retrosnub icosicosidodecahedron
Sirsid
V 60,E 180,F 112=(40+60){3}+12{5/2}
χ=−8, group=Ih, [5,3], *532
|3/2 3/2 5/2 - (35.5/3)/2
W118, U72, K77, C91
Small inverted retrosnub icosicosidodecahedron

I

Polyhedron snub 12-20 left max.png
Snub dodecahedron
Snid
V 60,E 150,F 92=(20+60){3}+12{5}
χ=2, group=I, 1/2H3, [5,3]+, (532), order 60
| 2 3 5 - 3.3.3.3.5
W18, U29, K34, C32

Snub dodecadodecahedron.png
Snub dodecadodecahedron
Siddid
V 60,E 150,F 84=60{3}+12{5}+12{5/2}
χ=−6, group=I, [5,3]+, 532
|2 5/2 5 - 3.3.5/2.3.5
W111, U40, K45, C49

Inverted snub dodecadodecahedron.png
Inverted snub dodecadodecahedron
Isdid
V 60,E 150,F 84=60{3}+12{5}+12{5/2}
χ=−6, group=I, [5,3]+, 532
|5/3 2 5 - 3.3.5.3.5/3
W114, U60, K65, C76

I

Great snub icosidodecahedron.png
Great snub icosidodecahedron
Gosid
V 60,E 150,F 92=(20+60){3}+12{5/2}
χ=2, group=I, [5,3]+, 532
|2 5/2 3 - 34.5/2
W116, U57, K62, C88

Great inverted snub icosidodecahedron.png
Great inverted snub icosidodecahedron
Gisid
V 60,E 150,F 92=(20+60){3}+12{5/2}
χ=2, group=I, [5,3]+, 532
|5/3 2 3 - 34.5/3
W113, U69, K74, C73

Great retrosnub icosidodecahedron.png
Great retrosnub icosidodecahedron
Girsid
V 60,E 150,F 92=(20+60){3}+12{5/2}
χ=2, group=I, [5,3]+, 532
|3/2 5/3 2 - (34.5/2)/2
W117, U74, K79, C90
Great inverted retrosnub icosidodecahedron

I

Snub icosidodecadodecahedron.png
Snub icosidodecadodecahedron
Sided
V 60,E 180,F 104=(20+60){3}+12{5}+12{5/2}
χ=−16, group=I, [5,3]+, 532
|5/3 3 5 - 3.3.3.5.3.5/3
W112, U46, K51, C58

Great snub dodecicosidodecahedron.png
Great snub dodecicosidodecahedron
Gisdid
V 60,E 180,F 104=(20+60){3}+(12+12){5/2}
χ=−16, group=I, [5,3]+, 532
| 5/3 5/2 3 - 3.3.3.5/2.3.5/3
W115, U64, K69, C80

Wythoff |p q r s[edit]

Symmetry group
Ih

Great dirhombicosidodecahedron.png
Great dirhombicosidodecahedron
Gidrid
V 60,E 240,F 124=40{3}+60{4}+24{5/2}
χ=−56, group=Ih, [5,3], *532
|3/2 5/3 3 5/2 - 4.5/3.4.3.4.5/2.4.3/2
W119, U75, K80, C92