User:Tomruen/List of uniform polyhedra and tilings2

See: User:Tomruen/polyhedron db testing

Triples

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Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
Tetrahedron   3 | 2 3
| 2 2 2
 
3.3.3
Tet Td, A3, [3,3], (*332) W1 U01 K06 4 6 4 2 4{3}  
Self-dual


triangular prism   2 3 | 2  
4.4.3
Trip D3h, [3,2], (*322), order 12 W-- U76(a) K01(a) 6 9 5 2 3{4}+2{3}  
Triangular dipyramid


Truncated tetrahedron   2 3 | 3  
3.6.6
Tut Td, A3, [3,3], (*332), order 24 W6 U02 K07 12 18 8 2 4{3}+4{6}  
Triakis tetrahedron


Truncated cube   2 3 | 4  
3.8.8
Tic Oh, B3, [4,3], (*432), order 48 W8 U09 K14 24 36 14 2 8{3}+6{8}  
Triakis octahedron


Truncated dodecahedron   2 3 | 5  
3.10.10
Tid Ih, H3, [5,3], (*532), order 120 W10 U26 K31 60 90 32 2 20{3}+12{10}  
Triakis icosahedron


Hexahedron   3 | 2 4  
4.4.4
Cube Oh, B3, [4,3], (*432) W3 U06 K11 8 12 6 2 6{4}  
Octahedron


Cube   2 4 | 2
2 2 2 |
 
4.4.4
Cube D4h, [4,2], (*422), order 16 W-- U76(b) K01(b) 8 12 6 2 4{4}+2{4}  
Octahedron


pentagonal prism   2 5 | 2  
4.4.5
Pip D5h, [5,2], (*522), order 20 W-- U76(c) K01(c) 10 15 7 2 5{4}+2{5}  
Pentagonal dipyramid


hexagonal prism   2 6 | 2
2 2 3 |
 
4.4.6
Hip D6h, [6,2], (*622), order 24 W-- U76(d) K01(d) 12 18 8 2 6{4}+2{6} File:Hexagonal bipyramid.png
Hexagonal dipyramid


octagonal prism   2 8 | 2
2 2 4 |
 
4.4.8
Op D8h, [8,2], (*822), order 32 W-- U76(f) K01(f) 16 24 10 2 8{4}+2{8}  
Octagonal dipyramid


decagonal prism   2 10 | 2
2 2 5 |
 
4.4.10
Dip D10h, [10,2], (*10.2.2), order 40 W-- U76(h) K01(h) 20 30 12 2 10{4}+2{10}  
Decagonal dipyramid


dodecagonal prism   2 12 | 2
2 2 6 |
 
4.4.12
Twip D12h, [12,2], (*12.2.2), order 48 W-- U76(j) K01(j) 24 36 14 2 12{4}+2{12} File:Dodecagonal dipyramid.png
Dodecagonal dipyramid


Truncated octahedron   2 4 | 3
3 3 2 |
 
4.6.6
Toe Oh, B3, [4,3], (*432), order 48
Th, [3,3] and (*332), order 24
W7 U08 K13 24 36 14 2 6{4}+8{6}  
Tetrakis hexahedron


Truncated cuboctahedron   2 3 4 |  
4.6.8
Girco Oh, B3, [4,3], (*432), order 48 W15 U11 K16 48 72 26 2 12{4}+8{6}+6{8}  
Disdyakis dodecahedron


Truncated icosidodecahedron   2 3 5 |  
4.6.10
Grid Ih, H3, [5,3], (*532), order 120 W16 U28 K33 120 180 62 2 30{4}+20{6}+12{10}  
Disdyakis triacontahedron


Dodecahedron   3 | 2 5  
5.5.5
Doe Ih, H3, [5,3], (*532) W5 U23 K28 20 30 12 2 12{5}  
Regular icosahedron


Truncated icosahedron   2 5 | 3  
5.6.6
Ti Ih, H3, [5,3], (*532), order 120 W9 U25 K30 60 90 32 2 12{5}+20{6}  
Pentakis dodecahedron


Quadruples

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Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
Octahedron   4 | 2 3  
3.3.3.3
Oct Oh, BC3, [4,3], (*432) W2 U05 K10 6 12 8 2 8{3}  
Cube


triangular antiprism   | 2 2 3  
3.3.3.3
Oct D3d, [6,2+], (2*3), order 18 W-- U77(a) K02(a) 6 12 8 2 6{3}+2{3}  
Trigonal trapezohedron


square antiprism   | 2 2 4  
3.3.3.4
Squap D4d, [2+,8], (2*4), order 16 W-- U77(b) K02(b) 8 16 10 2 8{3}+2{4}  
Tetragonal trapezohedron


pentagonal antiprism   | 2 2 5  
3.3.3.5
Pap D5d, [2+,10], (2*5), order 20 W-- U77(c) K02(c) 10 20 12 2 10{3}+2{5}  
Pentagonal trapezohedron


hexagonal antiprism   | 2 2 6  
3.3.3.6
Hap D6d, [2+,12], (2*6), order 24 W-- U77(d) K02(d) 12 24 14 2 12{3}+2{6}  
Hexagonal trapezohedron


octagonal antiprism   | 2 2 8  
3.3.3.8
Oap D8d, [2+,16], (2*8), order 32 W-- U77(f) K02(f) 16 32 18 2 16{3}+2{8}  
Octagonal trapezohedron


decagonal antiprism   | 2 2 10  
3.3.3.10
Dap D10d, [2+,20], (2*10), order 40 W-- U77(h) K02(h) 20 40 22 2 20{3}+2{10}  
Decagonal trapezohedron


dodecagonal antiprism   | 2 2 12  
3.3.3.12
Twap D12d, [2+,24], (2*12), order 48 W-- U77(j) K02(j) 24 48 26 2 24{3}+2{12}  
Dodecagonal trapezohedron


Cuboctahedron   2 | 3 4
3 3 | 2
 
3.4.3.4
Co Oh, B3, [4,3], (*432), order 48
Td, [3,3], (*332), order 24
W11 U07 K12 12 24 14 2 8{3}+6{4}  
Rhombic dodecahedron


Rhombicuboctahedron   3 4 | 2  
3.4.4.4
Sirco Oh, B3, [4,3], (*432), order 48 W13 U10 K15 24 48 26 2 8{3}+(6+12){4}  
Deltoidal icositetrahedron


Rhombicosidodecahedron   3 5 | 2  
3.4.5.4
Srid Ih, H3, [5,3], (*532), order 120 W14 U27 K32 60 120 62 2 20{3}+30{4}+12{5}  
Deltoidal hexecontahedron


Icosidodecahedron   2 | 3 5  
3.5.3.5
Id Ih, H3, [5,3], (*532), order 120 W12 U24 K29 30 60 32 2 20{3}+12{5}  
Rhombic triacontahedron


Pentuples

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Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
Icosahedron   5 | 2 3  
3.3.3.3.3
Ike Ih, H3, [5,3], (*532) W4 U22 K27 12 30 20 2 20{3}  
Regular dodecahedron


Snub cube   | 2 3 4  
3.3.3.3.4
Snic O, 1/2B3, [4,3]+, (432), order 24 W17 U12 K17 24 60 38 2 (8+24){3}+6{4}  
Pentagonal icositetrahedron


Snub dodecahedron   | 2 3 5  
3.3.3.3.5
Snid I, 1/2H3, [5,3]+, (532), order 60 W18 U29 K34 60 150 92 2 (20+60){3}+12{5}  
Pentagonal hexecontahedron


Nonconvex regulars

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Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
Great dodecahedron   52 | 2 5  
(55)/2
Gad Ih, H3, [5,3], (*532) W21 U35 K40 12 30 12 -6 12{5}  
Small stellated dodecahedron


Small stellated dodecahedron   5 | 2 52  
(52)5
Sissid Ih, H3, [5,3], (*532) W20 U34 K39 12 30 12 -6 12 5  
Great dodecahedron


Great icosahedron   52 | 2 3  
(35)/2
Gike Ih, H3, [5,3], (*532) W41 U53 K58 12 30 20 2 20{3}  
Great stellated dodecahedron


Great stellated dodecahedron   3 | 2 52  
(52)3
Gissid Ih, H3, [5,3], (*532) W22 U52 K57 20 30 12 2 12 { 52 }  
Great icosahedron


Nonconvex star prisms

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Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
pentagrammic prism   2 5/2 | 2  
4.4.5/2
Stip D5h, [5,2], (*522), order 20 W-- U78(a) K03(a) 10 15 7 2 5{4}+2{5/2} File:Pentagrammic dipyramid.png
Pentagrammic dipyramid


pentagrammic antiprism   | 2 2 5/2  
3.3.3.5/2
Stap D5h, [5,2], (*552), order 20 W-- U79(a) K04(a) 10 20 12 2 10{3}+2{5/2} File:Pentagrammic trapezohedron.png
Pentagrammic trapezohedron


pentagrammic crossed-antiprism   | 2 2 5/3  
3.3.3.5/3 or 3.3.3.-5/2
Starp D5h, [5,2], (*522), order 20 W-- U80(a) K05(a) 10 20 12 2 10{3}+2{5/2} File:Pentagrammic concave trapezohedron.png
Pentagrammic concave trapezohedron


Nonconvex stars by uniform index

edit
Name Picture Wythoff
symbol
Vertex figure Bowers-style
acronym
Sym.
grp
W# U# K# V E F χ Faces by type Dual
Octahemioctahedron   3/2 3 | 3  
3.6.3/2.6
Oho Oh, [4,3], *432 W68 U03 K08 12 24 12 0 8{3}+4{6}  
Octahemioctacron


Tetrahemihexahedron   3/2 3 | 2 (double-covering)  
3.4.3/2.4
Thah Td, [3,3], *332 W67 U04 K09 6 12 7 1 4{3}+3{4}  
Tetrahemihexacron


Small cubicuboctahedron   3/2 4 | 4
3 4/3 | 4
 
4.8.3/2.8
Socco Oh, [4,3], *432 W69 U13 K18 24 48 20 −4 8{3}+6{4}+6{8}  
Small hexacronic icositetrahedron


Great cubicuboctahedron   3 4 | 4/3
4 3/2 | 4
 
3.8/3.4.8/3
Gocco Oh, [4,3], *432 W77 U14 K19 24 48 20 −4 8{3}+6{4}+6{8/3}  
Great hexacronic icositetrahedron


Cubohemioctahedron   4/3 4 | 3 (double-covering)  
4.6.4/3.6
Cho Oh, [4,3], *432 W78 U15 K20 12 24 10 −2 6{4}+4{6}  
Hexahemioctacron


Cubitruncated cuboctahedron   3 4 4/3 |  
6.8.8/3
Cotco Oh, [4,3], *432 W79 U16 K21 48 72 20 −4 8{6}+6{8}+6{8/3}  
Tetradyakis hexahedron


Nonconvex great rhombicuboctahedron   3/2 4 | 2
3 4/3 | 2
 
4.4.4.3/2
Querco Oh, [4,3], *432 W85 U17 K22 24 48 26 2 8{3}+(6+12){4}  
Great deltoidal icositetrahedron


Small rhombihexahedron   2 4 (3/2 4/2) |  
4.8.4/3.8/7
Sroh Oh, [4,3], *432 W86 U18 K23 24 48 18 −6 12{4}+6{8}  
Small rhombihexacron


Stellated truncated hexahedron   2 3 | 4/3
2 3/2 | 4/3
 
3.8/3.8/3
Quith Oh, [4,3], *432 W92 U19 K24 24 36 14 2 8{3}+6{8/3}  
Great triakis octahedron


Great truncated cuboctahedron   2 3 4/3 |  
4.6/5.8/3
Quitco Oh, [4,3], *432 W93 U20 K25 48 72 26 2 12{4}+8{6}+6{8/3}  
Great disdyakis dodecahedron


Great rhombihexahedron   2 4/3 (3/2 4/2) |  
4.8/3.4/3.8/5
Groh Oh, [4,3], *432 W103 U21 K26 24 48 18 −6 12{4}+6{8/3}  
Great rhombihexacron


Small ditrigonal icosidodecahedron   3 | 5/2 3  
(3.5/2)3
Sidtid Ih, [5,3], *532 W70 U30 K35 20 60 32 −8 20{3}+12{5/2}  
Small triambic icosahedron


Small icosicosidodecahedron   5/2 3 | 3  
6.5/2.6.3
Siid Ih, [5,3], *532 W71 U31 K36 60 120 52 −8 20{3}+12{5/2}+20{6}  
Small icosacronic hexecontahedron


Small snub icosicosidodecahedron   | 5/2 3 3  
35.5/2
Seside Ih, [5,3], *532 W110 U32 K37 60 180 112 −8 (40+60){3}+12{5/2}  
Small hexagonal hexecontahedron


Small dodecicosidodecahedron   3/2 5 | 5
3 5/4 | 5
 
5.10.3/2.10
Saddid Ih, [5,3], *532 W72 U33 K38 60 120 44 −16 20{3}+12{5}+12{10}  
Small dodecacronic hexecontahedron


Dodecadodecahedron   2 | 5 5/2
2 | 5 5/3
2 | 5/2 5/4
2 | 5/3 5/4
 
5.5/2.5.5/2
Did Ih, [5,3], *532 W73 U36 K41 30 60 24 −6 12{5}+12{5/2}  
Medial rhombic triacontahedron


Truncated great dodecahedron   2 5/2 | 5
2 5/3 | 5
 
10.10.5/2
Tigid Ih, [5,3], *532 W75 U37 K42 60 90 24 −6 12{5/2}+12{10}  
Small stellapentakis dodecahedron


Rhombidodecadodecahedron   5/2 5 | 2  
4.5/2.4.5
Raded Ih, [5,3], *532 W76 U38 K43 60 120 54 −6 30{4}+12{5}+12{5/2}  
Medial deltoidal hexecontahedron


Small rhombidodecahedron   2 5 (3/2 5/2) |  
4.10.4/3.10/9
Sird Ih, [5,3], *532 W74 U39 K44 60 120 42 −18 30{4}+12{10}  
Small rhombidodecacron


Snub dodecadodecahedron   | 2 5/2 5  
3.3.5/2.3.5
Siddid I, [5,3]+, 532 W111 U40 K45 60 150 84 −6 60{3}+12{5}+12{5/2}  
Medial pentagonal hexecontahedron


Ditrigonal dodecadodecahedron   3 | 5/3 5
3/2 | 5 5/2
3/2 | 5/3 5/4
3 | 5/2 5/4
 
(5.5/3)3
Ditdid Ih, [5,3], *532 W80 U41 K46 20 60 24 −16 12{5}+12{5/2}  
Medial triambic icosahedron


Great ditrigonal dodecicosidodecahedron   3 5 | 5/3
5/4 3/2 | 5/3
 
3.10/3.5.10/3
Gidditdid Ih, [5,3], *532 W81 U42 K47 60 120 44 −16 20{3}+12{5}+12{10/3}  
Great ditrigonal dodecacronic hexecontahedron


Small ditrigonal dodecicosidodecahedron   5/3 3 | 5
5/2 3/2 | 5
 
3.10.5/3.10
Sidditdid Ih, [5,3], *532 W82 U43 K48 60 120 44 −16 20{3}+12{5/2}+12{10}  
Small ditrigonal dodecacronic hexecontahedron


Icosidodecadodecahedron   5/3 5 | 3
5/2 5/4 | 3
 
5.6.5/3.6
Ided Ih, [5,3], *532 W83 U44 K49 60 120 44 −16 12{5}+12{5/2}+20{6}  
Medial icosacronic hexecontahedron


Icositruncated dodecadodecahedron   3 5 5/3 |  
6.10.10/3
Idtid Ih, [5,3], *532 W84 U45 K50 120 180 44 −16 20{6}+12{10}+12{10/3}  
Tridyakis icosahedron


Snub icosidodecadodecahedron   | 5/3 3 5  
3.3.3.5.3.5/3
Sided I, [5,3]+, 532 W112 U46 K51 60 180 104 −16 (20+60){3}+12{5}+12{5/2}  
Medial hexagonal hexecontahedron


Great ditrigonal icosidodecahedron   3/2 | 3 5
3 | 3/2 5
3 | 3 5/4
3/2 | 3/2 5/4
 
((3.5)3)/2
Gidtid Ih, [5,3], *532 W87 U47 K52 20 60 32 −8 20{3}+12{5}  
Great triambic icosahedron


Great icosicosidodecahedron   3/2 5 | 3
3 5/4 | 3
 
5.6.3/2.6
Giid Ih, [5,3], *532 W88 U48 K53 60 120 52 −8 20{3}+12{5}+20{6}  
Great icosacronic hexecontahedron


Small icosihemidodecahedron   3/2 3 | 5 (double covering)  
3.10.3/2.10
Seihid Ih, [5,3], *532 W89 U49 K54 30 60 26 −4 20{3}+6{10}  
Small icosihemidodecacron


Small dodecicosahedron   3 5 (3/2 5/4) |  
6.10.6/5.10/9
Siddy Ih, [5,3], *532 W90 U50 K55 60 120 32 −28 20{6}+12{10}  
Small dodecicosacron


Small dodecahemidodecahedron   5/4 5 | 5 (double covering)  
5.10.5/4.10
Sidhid Ih, [5,3], *532 W91 U51 K56 30 60 18 −12 12{5}+6{10}  
Small dodecahemidodecacron


Great icosidodecahedron   2 | 3 5/2
2 | 3 5/3
2 | 3/2 5/2
2 | 3/2 5/3
 
3.5/2.3.5/2
Gid Ih, [5,3], *532 W94 U54 K59 30 60 32 2 20{3}+12{5/2}  
Great rhombic triacontahedron


Truncated great icosahedron   2 5/2 | 3
2 5/3 | 3
 
6.6.5/2
Tiggy Ih, [5,3], *532 W95 U55 K60 60 90 32 2 12{5/2}+20{6}  
Great stellapentakis dodecahedron


Rhombicosahedron   2 3 (5/4 5/2) |  
4.6.4/3.6/5
Ri Ih, [5,3], *532 W96 U56 K61 60 120 50 −10 30{4}+20{6}  
Rhombicosacron


Great snub icosidodecahedron   | 2 5/2 3  
34.5/2
Gosid I, [5,3]+, 532 W113 U57 K62 60 150 92 2 (20+60){3}+12{5/2}  
Great pentagonal hexecontahedron


Small stellated truncated dodecahedron   2 5 | 5/3
2 5/4 | 5/3
 
5.10/3.10/3
Quit Sissid Ih, [5,3], *532 W97 U58 K63 60 90 24 −6 12{5}+12{10/3}  
Great pentakis dodecahedron


Truncated dodecadodecahedron   2 5 5/3 |  
4.10/9.10/3
Quitdid Ih, [5,3], *532 W98 U59 K64 120 180 54 −6 30{4}+12{10}+12{10/3}  
Medial disdyakis triacontahedron


Inverted snub dodecadodecahedron   | 5/3 2 5  
3.3.5.3.5/3
Isdid I, [5,3]+, 532 W114 U60 K65 60 150 84 −6 60{3}+12{5}+12{5/2}  
Medial inverted pentagonal hexecontahedron


Great dodecicosidodecahedron   5/2 3 | 5/3
5/3 3/2 | 5/3
 
3.10/3.5/2.10/7
Gaddid Ih, [5,3], *532 W99 U61 K66 60 120 44 −16 20{3}+12{5/2}+12{10/3}  
Great dodecacronic hexecontahedron


Small dodecahemicosahedron   5/3 5/2 | 3 (double covering)  
6.5/2.6.5/3
Sidhei Ih, [5,3], *532 W100 U62 K67 30 60 22 −8 12{5/2}+10{6}  
Small dodecahemicosacron


Great dodecicosahedron   3 5/3 (3/2 5/2) |  
6.10/3.6/5.10/7
Giddy Ih, [5,3], *532 W101 U63 K68 60 120 32 −28 20{6}+12{10/3}  
Great dodecicosacron


Great snub dodecicosidodecahedron   | 5/3 5/2 3  
3.3.3.5/2.3.5/3
Gisdid I, [5,3]+, 532 W115 U64 K69 60 180 104 −16 (20+60){3}+(12+12){5/2}  
Great hexagonal hexecontahedron


Great dodecahemicosahedron   5/4 5 | 3 (double covering)  
5.6.5/4.6
Gidhei Ih, [5,3], *532 W102 U65 K70 30 60 22 −8 12{5}+10{6}  
Great dodecahemicosacron


Great stellated truncated dodecahedron   2 3 | 5/3  
3.10/3.10/3
Quit Gissid Ih, [5,3], *532 W104 U66 K71 60 90 32 2 20{3}+12{10/3}  
Great triakis icosahedron


Nonconvex great rhombicosidodecahedron   5/3 3 | 2
5/2 3/2 | 2
 
3.4.5/3.4
Qrid Ih, [5,3], *532 W105 U67 K72 60 120 62 2 20{3}+30{4}+12{5/2}  
Great deltoidal hexecontahedron


Great truncated icosidodecahedron   2 3 5/3 |  
4.6.10/3
Gaquatid Ih, [5,3], *532 W108 U68 K73 120 180 62 2 30{4}+20{6}+12{10/3}  
Great disdyakis triacontahedron


Great inverted snub icosidodecahedron   | 5/3 2 3  
34.5/3
Gisid I, [5,3]+, 532 W116 U69 K74 60 150 92 2 (20+60){3}+12{5/2}  
Great inverted pentagonal hexecontahedron


Great dodecahemidodecahedron   5/3 5/2 | 5/3 (double covering)  
5/2.10/3.5/3.10/3
Gidhid Ih, [5,3], *532 W107 U70 K75 30 60 18 −12 12{5/2}+6{10/3}  
Great dodecahemidodecacron


Great icosihemidodecahedron   3/2 3 | 5/3  
3.10/3.3/2.10/3
Geihid Ih, [5,3], *532 W106 U71 K76 30 60 26 −4 20{3}+6{10/3}  
Great icosihemidodecacron


Small retrosnub icosicosidodecahedron   | 3/2 3/2 5/2  
(35.5/3)/2
Sirsid Ih, [5,3], *532 W118 U72 K77 60 180 112 −8 (40+60){3}+12{5/2}  
Small hexagrammic hexecontahedron


Great rhombidodecahedron   2 5/3 (3/2 5/4) |  
4.10/3.4/3.10/7
Gird Ih, [5,3], *532 W109 U73 K78 60 120 42 −18 30{4}+12{10/3}  
Great rhombidodecacron


Great retrosnub icosidodecahedron   | 2 3/2 5/3  
(34.5/2)/2
Girsid I, [5,3]+, 532 W117 U74 K79 60 150 92 2 (20+60){3}+12{5/2}  
Great pentagrammic hexecontahedron


Great dirhombicosidodecahedron   | 3/2 5/3 3 5/2  
4.5/3.4.3.4.5/2.4.3/2
Gidrid Ih, [5,3], *532 W119 U75 K80 60 240 124 −56 40{3}+60{4}+24{5/2}  
Great dirhombicosidodecacron


Great disnub dirhombidodecahedron   | (3/2) 5/3 (3) 5/2  
(5/2.4.3.3.3.4. 5/3.4.3/2.3/2.3/2.4)/2
Gidisdrid Ih, [5,3], *532 W- U- K- 60 360 204 −96 120{3}+60{4}+24{5/2}  
Great disnub dirhombidodecacron