See: User:Tomruen/polyhedron db testing
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
|
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
|
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
|
Name | Picture | Wythoff symbol |
Vertex figure |
Bowers-style acronym |
Sym. grp |
W# | U# | K# | V | E | F | χ | Faces by type | Dual |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Great dodecahedron | 5⁄2 | 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 5⁄2 |
(5⁄2)5 |
Sissid | Ih, H3, [5,3], (*532) | W20 | U34 | K39 | 12 | 30 | 12 | -6 | 12 5 |
Great dodecahedron
| |
Great icosahedron | 5⁄2 | 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 5⁄2 |
(5⁄2)3 |
Gissid | Ih, H3, [5,3], (*532) | W22 | U52 | K57 | 20 | 30 | 12 | 2 | 12 { 5⁄2 } |
Great icosahedron
|
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
|
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
|
See: User:Tomruen/polyhedron db testing
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
|
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
|
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
|
Name | Picture | Wythoff symbol |
Vertex figure |
Bowers-style acronym |
Sym. grp |
W# | U# | K# | V | E | F | χ | Faces by type | Dual |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Great dodecahedron | 5⁄2 | 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 5⁄2 |
(5⁄2)5 |
Sissid | Ih, H3, [5,3], (*532) | W20 | U34 | K39 | 12 | 30 | 12 | -6 | 12 5 |
Great dodecahedron
| |
Great icosahedron | 5⁄2 | 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 5⁄2 |
(5⁄2)3 |
Gissid | Ih, H3, [5,3], (*532) | W22 | U52 | K57 | 20 | 30 | 12 | 2 | 12 { 5⁄2 } |
Great icosahedron
|
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
|
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
|