Uniform Polyhedra 

Notes:

The list of uniform polyhedra was first published by H.S.M.Coxeter, M.S.Longuet-Higgins and J.C.P.Miller in "Uniform Polyhedra", published in Philosophical Transactions of the Royal Society of London, Series A Volume 246 pp 401-450 (1954).  

Prisms (other than the pentagonal examples shown below) are shown separately here.  Skilling's figure is linked here.

More information on the Wythoff symbol and the TOCID notation is linked here, I am indebted to Dr Norman Johnson for providing the linked information.

The table below lists all of the Uniform Polyhedra.  All links are to HEDRON 'switchable' VRML files.  The 'mol' column links to molecular files. 

"Wenn No." refers to the number of the polyhedron in Magnus Wenninger's "Polyhedron Models", Cambridge University Press, 1971.

Note: Colour coding and bold figures on vertex descriptions are my own addition.  Star polygons are shown in black, normal polygons in red, retrograde polygons in bold (black or red). Factors of 2 for vertices which wrap twice around the axis are shown in blue.

Back: To Index

No Vertex Wythoff
Symbol		 Name
.............................................................		 Mol TOCID Abbrev. Wenn
No.		 Alt Names (Green=Wenninger)
and links to other pages on this site.
01 n,4,4  2 n | 2 Pentagonal Prism mol nP Pip   Link to: Isogonal Deltahedra
02 n,3,3,3  | 2 2 n Pentagonal Anti-prism mol nQ Pap    
03 n/d,4,4  2 n/d | 2 Pentagrammic Prism mol nP* or n/dP Stip   Link to: Isogonal Deltahedra 
04 n/d,3,3,3  | 2 2 n/d Pentagrammic Anti-Prism mol nQ* or n/dQ Stap    
05 n/(n-d),3,3,3  | 2 2 n/(n-d) Pentagrammic Crossed Anti-Prism mol nR* or n/dR Sistap    
06 3,3,3  3 | 2 3 Tetrahedron mol T Tet 1 Link to: Isogonal Deltahedra
Link to: Rhombified Stellations of Snubs
07 6,6,3  2 3 | 3 Truncated Tetrahedron  mol tT Tut 6  
08 3,6,3/2,6  3/2 3 | 3 Octahemioctahedron mol O|C or aTT Oho 68  
09 3,4,3/2,4  3/2 3 | 2 Tetrahemihexahedron mol T|T Thah 67 "One sided heptahedron"
10 3,3,3,3  4 | 2 3 Octahedron mol O Oct 2 Link to: Stewart Toroid: Ring of 8 octahedra 
Link to: Augmented forms
Link to: [3,3] twister
Link to: Isogonal Deltahedra
Link to: Rhombified Stellations of Snubs
11 4,4,4   3 | 2 4 Cube mol C Cube 3 Link to: Augmented forms
Link to: Isogonal Deltahedra
Link to: Isogonal Rhombihedra
Link to: Rhombified Stellations of Snubs
Link to: Edge Rhombified Polyhedra
12  4,3,4,3  2 | 3 4 Cuboctahedron mol CO or rTT Co 11 Link to: Augmented Dual Toroids
Link to: [3,3] twister and [4.3]-twister
Link to: Isogonal Deltahedra
Link to: Isogonal Rhombihedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
13  6,6,4  2 4 | 3 Truncated Octahedron mol tO or tTT Toe 7  
14 8,8,3   2 3 | 4 Truncated Cube mol tC Tic 8  
15 4,4,4,3  3 4 | 2 Rhombicuboctahedron mol rCO Sirco 13 Small Rhombicuboctahedron
Link to: isomorphs 
Link to: [4,3] twister
16 8,6,4  2 3 4 | Truncated Cuboctahedron mol tCO Girco 15 Rhombitruncated Cuboctahedron
Link to: Stewart Toroids "K4 world" 
Link to: Canonical Toroid
17 4,3,3,3,3   | 2 3 4 Snub Cuboctahedron mol sCO Snic 17 Snub Cube
Link to: tetrakis snub prisms
Link to: [4,3] twister
Link to: Rhombified Stellations of Snubs
18 4,8,3/2,8  3/2 4 | 4 Small Cubicuboctahedron mol bCO Socco 69  
19 4,8/3,3,8/3  3 4 | 4/3 Great Cubicuboctahedron mol cOC* Gocco 77 Link to: Augmented forms
Link to: formed by cupolas
20 4,6,4/3,6   4/3 4 | 3 Cubohemioctahedron mol C|O or ra|TT Cho 78  
21 8/3,6,8   4/3 3 4 | Cubitruncated Cuboctahedron mol tCC* Cotco 79 Cuboctatruncated Cuboctahedron
Link to: Augmented forms
22 4,3/2,4,4   3/2 4 | 2 Great Rhombicuboctahedron mol rOC* Querco 85 Quasirhombicuboctahedron
Link to: formed by cupolas
Link to: Augmented forms
23 8,4,8/7,4/3   3/2 2 4 | Small Rhombicube mol rb|CO Sroh 86 Small Rhombihexahedron
24 8/3,8/3,3  2 3 | 4/3 Stellatruncated Cube mol tC* Quith 92 Stellated Truncated Hexahedron,
Quasitruncated Hexahedron
Link to: Augmented forms
25 6,4,8/3  4/3 2 3 | Great Truncated Cuboctahedron mol tOC* Quitco 93 Quasitruncated Cuboctahedron
Stellatruncated Cuboctahedron
Link to: Augmented forms
26 8/3,4,8/5,4/3  3/2 4 | 2 Great Rhombicube mol rc|OC* Groh 103 Great Rhombihexahedron
Link to: formed by cupolas
27 3,3,3,3,3   5 | 2 3 Icosahedron mol I or sTT Ike 4 Link to: isomorphs 
Link to: Augmented form
Link to: [3,3] twister
Link to: Isogonal Deltahedra
Link to: Rhombified Stellations of Snubs
28 5,5,5  3 | 2 5 Dodecahedron mol D Doe 5 Link to: Augmented form
Link to: Isogonal Deltahedra
Link to: Rhombified Stellations of Snubs
Link to: Edge Rhombified Polyhedra
29 5,3,5,3  2 | 3 5 Icosidodecahedron mol ID Id 12 Link to: Augmented Dual Toroids
Link to: [5,3] twister
Link to: Isogonal Deltahedra
Link to: Isogonal Rhombihedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
30 6,6,5  2 5 | 3 Truncated Icosahedron mol tI Ti 9  
31 10,10,3  2 3 | 5 Truncated Dodecahedron mol tD Tid 10 Link to: Stewart Toroids "T5 country" 
32 5,4,3,4  3 5 | 2 Rhombicosidodecahedron (small) mol rID Srid 14 Link to: Canonical Toroid
Link to: [5,3] twister
Link to: Isogonal Rhombihedra
33 10,6,4  2 3 5 | Truncated Icosidodecahedron mol tID Grid 16 Rhombitruncated Icosidodecahedron, 
Great Rhombicosidodecahedron
Link to: Canonical Toroid
34 5,3,3,3,3  | 2 3 5 Snub Icosidodecahedron mol sID Snid 18 Snub Dodecahedron
Link to: pentakis snub pentaprisms
Link to: [5,3] twister
Link to: Rhombified Stellations of Snubs
35 3,5/2,3,5/2,3,5/2  3 | 5/2 3 Small Ditrigonal Icosidodecahedron mol ID* Sidtid 70 Link to: 5/2 cuploid
Link to: Augmented forms
Link to: Isogonal Deltahedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
36 3,6,5/2,6  5/2 3 | 3 Small Icosicosidodecahedron mol iID* Siid 71 Small Icosic icosidodecahedron
Small icosified icosidodecahedron
Link to: Isogonal Rhombihedra
37 5/2,3,3,3,3,3  | 5/2 3 3 Snub Disicosidodecahedron mol sID* Seside 110 Small Snub Icosicosidodecahedron
Link to: Rhombified Stellations of Snubs
38 5,10,3/2,10  3/2 5 | 5 Small Dodecicosidodecahedron mol dID Saddid 72 Link to: Isogonal Rhombihedra 
39 5/2,5/2,5/2,5/2,5/2  5 | 2 5/2 Small Stellated Dodecahedron mol D* Sissid 20 Link to: Augmented forms
Link to: Isogonal Deltahedra
Link to: Edge Rhombified Polyhedra
40 (5,5,5,5,5)/2  5/2 | 2 5 Great Dodecahedron mol E Gad 21 Link to: Augmented forms
Link to: Edge Rhombified Polyhedra
41 5/2,5,5/2,5   2 | 5/2 5 Dodecadodecahedron mol ED* Did 73 Link to: Augmented forms
Link to: Augmented Dual Toroids
Link to: [5/2,5] twister and [5/3,5] twister
Link to: Isogonal Deltahedra
Link to: Isogonal Rhombihedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
42 10,10,5/2   2 | 5/2 5 Great Truncated Dodecahedron  mol tE Tigid 75 Truncated Great Dodecahedron
43 5,4,5/2,4   5/2 5 | 2 Rhombidodecadodecahedron mol rED* Raded 76 Link to: [5/2,5] twister
Link to: Isogonal Rhombihedra
44 4,10,4/3,10/9   2 5/2 5 | Small Rhombidodecahedron  mol rd|ID Sird 74  
45 5/2,3,5,3,3   | 2 5/2 5 Snub Dodecadodecahedron  mol sED* Siddid 111 Link to: Augmented forms
Link to: [5/2,5] twister
Link to: Rhombified Stellations of Snubs
46  5/3,5,5/3,5,5/3,5   3 | 5/3 5 Ditrigonary Dodecadodecahedron  mol DE* Ditdid 80 Link to: 5/2 cuploid
Link to: Augmented forms
Link to: Isogonal Deltahedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
47 5,10/3,3,10/3   3 5 | 5/3 Great Dodekified Icosidodecahedron  mol eJE Gidditdid 81 Great Ditrigonal Dodecicosidodecahedron
Link to: Augmented forms
48 3,10,5/3,10   5/3 3 | 5 Small Dodekified Icosidodecahedron mol dID* Sidditdid 82 Small Ditrigonal Dodecicosidodecahedron
49 5,6,5/3,6   5/3 5 | 3 Icosified Dodecadodecahedron  mol iED* Ided 83 Icosidodecadodecahedron
Link to: Isogonal Rhombihedra
50 10,6,10/3   5/3 3 5 | Icositruncated Dodecadodecahedron  mol tDE* Itdid 84 Icosidodecatruncated Icosidodecahedron
Link to: Augmented forms
51  5/3,3,5,3,3,3  | 5/3 3 5 Snub Icosidodecadodecahedron mol sDE* Sided 112 Icosisnub dodecadodecahedron 
52 (5,3,5,3,5,3)/2   3/2 | 3 5 Great Ditrigonary Icosidodecahedron  mol JE Gidtid 87 Link to: 5/2 cuploid
Link to: Augmented forms
Link to: Isogonal Deltahedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
53 5,6,3/2,6   3/2 5 | 3 Great Icosified Icosidodecahedron  mol iJE Giid 88 Great Icosicosidodecahedron
Link to: Isogonal Rhombihedra
54 3,10,3/2,10  3/2 3 | 5 Small Icosihemidodecahedron  mol I|D Seihid 89  
55 6,10,6/5,10/9   5/3 5/2 3 | Small Dodekicosahedron  mol di|ID* Siddy 90  
56 5,10,5/4,10  5/4 5 | 5 Small Dodecahemidodecahedron mol D|I Sidhid 91  
57 5/2,5/2,5/2  3 | 2 5/2 Great Stellated Dodecahedron mol E* Gissid 22 Link to: Augmented forms
58 (3,3,3,3,3)/2  5/2 | 2 3 Great Icosahedron  mol J or s*TT or s*O Gike 41 Link to: isomorphs
Link to: Augmented forms
Link to: Isogonal Deltahedra
59 5/2,3,5/2,3  3/2 5 | 3 Great Icosidodecahedron mol JE* Gid 94 Link to: isomorph,
Link to: Augmented forms
Link to: Augmented Dual Toroids
Link to: [5/3,3] twister and [5/2,3] twister
Link to: Isogonal Deltahedra
Link to: Isogonal Rhombihedra
Link to: Rhombically Expanded Deltahedra
Link to: Edge Rhombified Polyhedra
60 6,6,5/2   2 5/2 | 3 Great Truncated Icosahedron mol tJ Tiggy 95 Truncated Great Icosahedron
Link to: Isogonal Deltahedra
61 6,4,6/5,4/3   2 5/2 3 | Rhombicosahedron mol ri|ED* Ri 96  
62 5/2,3,3,3,3  | 2 5/2 3 Great Snub Icosidodecahedron mol sJE* Gosid 113 Great Inverted Snub Icosidodecahedron
Link to: [5/2,3] twister
63 10/3,10/3,5   2 5 | 5/3 Small Stellatruncated Dodecahedron mol tD* Quit Sissid 97 Small Stellated Truncated Dodecahedron
Quasitruncated Small Stellated Dodecahedron
64 10,10/3,4   5/3 2 5 | Stellatruncated Dodecadodecahedron mol tED* Quitdid 98 Quasitruncated Dodecahedron,
Truncated Dodecadodecahedron
65 5/3,3,5,3,3  | 5/3 2 5 Vertisnub Dodecadodecahedron mol s'ED* Isdid 114 Inverted Snub Dodecadodecahedron
Link to: Augmented forms
Link to: [5/3,5] twister
66 10/3,5/2,10/3,3   5/2 3 | 5/3 Great Dodekicosidodecahedron  mol eJE* Gaddid 99 Link to: Augmented forms
Link to: Isogonal Rhombihedra
67 5/2,6,5/3,6   5/3 5/2 | 3 Small Dodecahemicosahedron mol E|D* Sidhei 102  
68 10/3,6,10/7,6/5   5/3 5/2 3 | Great Dodekicosahedron mol ei|JE Giddy 101  
69 5/3,3,5/2,3,3,3   | 2 5/2 3 Great Snub Icosidisdodecahedron  mol SJE* Gisdid 115 Great Snub Dodecicosidodecahedron
Great Dodecasnub icosidodecahedron
Link to: Isomorphs
Link to: Augmented forms
Link to: Rhombified Stellations of Snubs
70 6,5,6,5/4   5/4 5 | 3 Great Dodecahemicosahedron mol D*|E Gidhei 100  
71 3,10/3,10/3  2 3 | 5/3 Great Stellatruncated Dodecahedron mol tE* Quit Gissid 104 Great Stellated Truncated Dodecahedron,
Quasitruncated Great Stellated Dodecahedron
Link to: Augmented forms
72 4,5/3,4,3   5/3 3 | 2 Great Rhombicosidodecahedron  mol rJE* Qrid 105 Quasirhombicosidodecahedron
Link to: Augmented forms
Link to: [5/3,3] twister
73 6,10/3,4  5/3 2 3 | Stellatruncated Icosidodecahedron mol tJE* Gaquatid 108 Great Truncated Icosidodecahedron,
Great Quasitruncated Icosidodecahedron
Link to: Isogonal Deltahedra
74 5/3,3,3,3,3   | 5/3 2 3  Great Vertisnub Icosidodecahedron mol s'JE* Gisid 116 Great Inverted Snub Icosidodecahedron
Link to: Augmented forms
Link to: [5/3,3] twister
Link to: Rhombified Stellations of Snubs
75 5/2,10/3,5/3,10/3  5/4 5 | 5 Great Dodecahemidodecahedron mol E*|J Gidhid 107  
76 3,10/3,3/2,10/3   3/2 3 | 5 Great Icosihemidodecahedron mol J|E* Geihid 106  
77 (5/3,3,3,3,3,3)/2  | 3/2 3/2 5/2 Small Retrosnub Icosicosidodecahedron  mol s*ID* Sirsid 118 Small Inverted Retrosnub Icosicosidodecahedron,
(Small) Retrosnub Disicosidodecahedron
Yog Sothoth
Link to: Augmented forms
78 10/3,4,10/7,4/3   3/2 5/3 2 | Great Rhombidodecahedron mol re|JE* Gird 109  
79 (5/2,3,3,3,3)/2   | 3/2 5/3 2 Great Retrosnub Icosidodecahedron mol s*JE* Girsid 117 Great Inverted Retrosnub Icosidodecahedron
Link to: pentakis great retrosnub {7/3} pentaprism
Link to: Augmented forms
80 (5/2,4,3,4, 5/3,4,3/2,4)/2   | 3/2 5/3 3
   5/2		 Great Disnub Disicosidisdodecahedron mol SSJE* Gidrid 119 Great Dirhombicosidodecahedron,
Miller's Monster