List of Wenninger polyhedron models

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This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.

The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.

It contains the 75 nonprismatic uniform polyhedra, as well as 44 stellated forms of the convex regular and quasiregular polyhedra.

This list was written to honor this early polyhedral work from Wenninger, and to provide a detailed reference to the 119 numbered models in his book.

Models listed here can be cited as "Wenninger Model Number N", or WN for brevity.

The polyhedra are grouped below in 5 tables: Regular (1–5), Semiregular (6–18), regular star polyhedra (20–22,41), Stellations and compounds (19–66), and uniform star polyhedra (67–119). The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings.

Platonic solids (regular) W1 to W5[edit]

Index Name Picture Dual name Dual picture Wythoff symbol Vertex figure
and Schläfli symbol
Symmetry group U# K# V E F Faces by type
1 Tetrahedron Tetrahedron.png Tetrahedron Tetrahedron.png 3|2 3 Tetrahedron vertfig.png
{3,3}
Td U01 K06 4 6 4 4{3}
2 Octahedron Octahedron.png Hexahedron Hexahedron.png 4|2 3 Octahedron vertfig.png
{3,4}
Oh U05 K10 6 12 8 8{3}
3 Hexahedron (Cube) Hexahedron.png Octahedron Octahedron.png 3|2 4 Cube vertfig.png
{4,3}
Oh U06 K11 8 12 6 6{4}
4 Icosahedron Icosahedron.png Dodecahedron Dodecahedron.png 5|2 3 Icosahedron vertfig.png
{3,5}
Ih U22 K27 12 30 20 20{3}
5 Dodecahedron Dodecahedron.png Icosahedron Icosahedron.png 3|2 5 Dodecahedron vertfig.png
{5,3}
Ih U23 K28 20 30 12 12{5}

Archimedean solids (Semiregular) W6 to W18[edit]

Index Name Picture Dual name Dual picture Wythoff symbol Vertex figure Symmetry group U# K# V E F Faces by type
6 Truncated tetrahedron Truncated tetrahedron.png triakis tetrahedron Triakis tetrahedron 2 3|3 Truncated tetrahedron vertfig.png
3.6.6
Td U02 K07 12 18 8 4{3} + 4{6}
7 Truncated octahedron Truncated octahedron.png tetrakis hexahedron Tetrakis hexahedron 2 4|3 Truncated octahedron vertfig.png
4.6.6
Oh U08 K13 24 36 14 6{4} + 8{6}
8 Truncated hexahedron Truncated hexahedron.png triakis octahedron Triakis octahedron 2 3|4 Truncated cube vertfig.png
3.8.8
Oh U09 K14 24 36 14 8{3} + 6{8}
9 Truncated icosahedron Truncated icosahedron.png pentakis dodecahedron Pentakis dodecahedron 2 5|3 Truncated icosahedron vertfig.png
5.6.6
Ih U25 K30 60 90 32 12{5} + 20{6}
10 Truncated dodecahedron Truncated dodecahedron.png triakis icosahedron Triakis icosahedron 2 3|5 Truncated dodecahedron vertfig.png
3.10.10
Ih U26 K31 60 90 32 20{3} + 12{10}
11 Cuboctahedron Cuboctahedron.png rhombic dodecahedron Rhombic dodecahedron 2|3 4 Cuboctahedron vertfig.png
3.4.3.4
Oh U07 K12 12 24 14 8{3} + 6{4}
12 Icosidodecahedron Icosidodecahedron.png rhombic triacontahedron Rhombic triacontahedron 2|3 5 Icosidodecahedron vertfig.png
3.5.3.5
Ih U24 K29 30 60 32 20{3} + 12{5}
13 Small rhombicuboctahedron Small rhombicuboctahedron.png deltoidal icositetrahedron Deltoidal icositetrahedron 3 4|2 Small rhombicuboctahedron vertfig.png
3.4.4.4
Oh U10 K15 24 48 26 8{3}+(6+12){4}
14 Small rhombicosidodecahedron Small rhombicosidodecahedron.png deltoidal hexecontahedron Deltoidal hexecontahedron 3 5|2 Small rhombicosidodecahedron vertfig.png
3.4.5.4
Ih U27 K32 60 120 62 20{3} + 30{4} + 12{5}
15 Truncated cuboctahedron
(Great rhombicuboctahedron)
Great rhombicuboctahedron.png disdyakis dodecahedron Disdyakis dodecahedron 2 3 4| Great rhombicuboctahedron vertfig.png
4.6.8
Oh U11 K16 48 72 26 12{4} + 8{6} + 6{8}
16 Truncated icosidodecahedron
(Great rhombicosidodecahedron)
Great rhombicosidodecahedron.png disdyakis triacontahedron Disdyakis triacontahedron 2 3 5| Great rhombicosidodecahedron vertfig.png
4.6.10
Ih U28 K33 120 180 62 30{4} + 20{6} + 12{10}
17 Snub cube Snub hexahedron.png pentagonal icositetrahedron Pentagonal icositetrahedron |2 3 4 Snub cube vertfig.png
3.3.3.3.4
O U12 K17 24 60 38 (8 + 24){3} + 6{4}
18 Snub dodecahedron Snub dodecahedron ccw.png pentagonal hexecontahedron Pentagonal hexecontahedron |2 3 5 Snub dodecahedron vertfig.png
3.3.3.3.5
I U29 K34 60 150 92 (20 + 60){3} + 12{5}

Kepler–Poinsot polyhedra (Regular star polyhedra) W20, W21, W22 and W41[edit]

Index Name Picture Dual name Dual picture Wythoff symbol Vertex figure
and Schläfli symbol
Symmetry group U# K# V E F Faces by type
20 Small stellated dodecahedron Small stellated dodecahedron.png Great dodecahedron Great dodecahedron.png 5|25/2 Small stellated dodecahedron vertfig.png
{5/2,5}
Ih U34 K39 12 30 12 12{5/2}
21 Great dodecahedron Great dodecahedron.png Small stellated dodecahedron Small stellated dodecahedron.png 5/2|2 5 Great dodecahedron vertfig.png
{5,5/2}
Ih U35 K40 12 30 12 12{5}
22 Great stellated dodecahedron Great stellated dodecahedron.png Great icosahedron Great icosahedron.png 3|25/2 Great stellated dodecahedron vertfig.png
{5/2,3}
Ih U52 K57 20 30 12 12{5/2}
41 Great icosahedron
(16th stellation of icosahedron)
Great icosahedron.png Great stellated dodecahedron Great stellated dodecahedron.png 5/2|2 3 Great icosahedron vertfig.png
{3,5/2}
Ih U53 K58 12 30 20 20{3}

Stellations: models W19 to W66[edit]

Stellations of octahedron[edit]

Index Name Symmetry group Picture Facets
2 Octahedron
(regular)
Oh Zeroth stellation of octahedron.png Zeroth stellation of octahedron facets.png
19 Stellated octahedron
(Compound of two tetrahedra)
Oh First stellation of octahedron.png Stellation of octahedron facets.png

Stellations of dodecahedron[edit]

Index Name Symmetry group Picture Facets
5 Dodecahedron (regular) Ih Zeroth stellation of dodecahedron.png Zeroth stellation of dodecahedron facets.svg
20 Small stellated dodecahedron (regular)
(First stellation of dodecahedron)
Ih First stellation of dodecahedron.png First stellation of dodecahedron facets.svg
21 Great dodecahedron (regular)
(Second stellation of dodecahedron)
Ih Second stellation of dodecahedron.png Second stellation of dodecahedron facets.svg
22 Great stellated dodecahedron (regular)
(Third stellation of dodecahedron)
Ih Third stellation of dodecahedron.png Third stellation of dodecahedron facets.svg

Stellations of icosahedron[edit]

Index Name Symmetry group Picture Facets
4 Icosahedron (regular) Ih Zeroth stellation of icosahedron.png Zeroth stellation of icosahedron facets.png
23 Compound of five octahedra
(First compound stellation of icosahedron)
Ih First compound stellation of icosahedron.png First compound stellation of icosahedron facets.png
24 Compound of five tetrahedra
(Second compound stellation of icosahedron)
I Second compound stellation of icosahedron.png Second compound stellation of icosahedron facets.png
25 Compound of ten tetrahedra
(Third compound stellation of icosahedron)
Ih Third compound stellation of icosahedron.png Third compound stellation of icosahedron facets.png
26 Small triambic icosahedron
(First stellation of icosahedron)
(Triakis icosahedron)
Ih First stellation of icosahedron.png First stellation of icosahedron facets.png
27 Second stellation of icosahedron Ih Second stellation of icosahedron.png Second stellation of icosahedron facets.png
28 Excavated dodecahedron
(Third stellation of icosahedron)
Ih Third stellation of icosahedron.png Third stellation of icosahedron facets.png
29 Fourth stellation of icosahedron Ih Fourth stellation of icosahedron.png Fourth stellation of icosahedron facets.png
30 Fifth stellation of icosahedron Ih Fifth stellation of icosahedron.png Fifth stellation of icosahedron facets.png
31 Sixth stellation of icosahedron Ih Sixth stellation of icosahedron.png Sixth stellation of icosahedron facets.png
32 Seventh stellation of icosahedron Ih Seventh stellation of icosahedron.png Seventh stellation of icosahedron facets.png
33 Eighth stellation of icosahedron Ih Eighth stellation of icosahedron.png Eighth stellation of icosahedron facets.png
34 Ninth stellation of icosahedron
Great triambic icosahedron
Ih Ninth stellation of icosahedron.png Ninth stellation of icosahedron facets.png
35 Tenth stellation of icosahedron I Tenth stellation of icosahedron.png Tenth stellation of icosahedron facets.png
36 Eleventh stellation of icosahedron I Eleventh stellation of icosahedron.png Eleventh stellation of icosahedron facets.png
37 Twelfth stellation of icosahedron Ih Twelfth stellation of icosahedron.png Twelfth stellation of icosahedron facets.png
38 Thirteenth stellation of icosahedron I Thirteenth stellation of icosahedron.png Thirteenth stellation of icosahedron facets.png
39 Fourteenth stellation of icosahedron I Fourteenth stellation of icosahedron.png Fourteenth stellation of icosahedron facets.png
40 Fifteenth stellation of icosahedron I Fifteenth stellation of icosahedron.png Fifteenth stellation of icosahedron facets.png
41 Great icosahedron (regular)
(Sixteenth stellation of icosahedron)
Ih Sixteenth stellation of icosahedron.png Sixteenth stellation of icosahedron facets.png
42 Final stellation of the icosahedron Ih Seventeenth stellation of icosahedron.png Seventeenth stellation of icosahedron facets.png

Stellations of cuboctahedron[edit]

Index Name Symmetry group Picture Facets (octahedral planes) Facets (cube planes)
11 Cuboctahedron (regular) Oh Zeroth stellation of cuboctahedron.png Zeroth stellation of cuboctahedron facets.png Zeroth stellation of cuboctahedron square facets.png
43 Compound of cube and octahedron
(First stellation of cuboctahedron)
Oh First stellation of cuboctahedron.png First stellation of cuboctahedron trifacets.png First stellation of cuboctahedron square facets.png
44 Second stellation of cuboctahedron Oh Second stellation of cuboctahedron.png Second stellation of cuboctahedron trifacets.png Second stellation of cuboctahedron square facets.png
45 Third stellation of cuboctahedron Oh Third stellation of cuboctahedron.png Third stellation of cuboctahedron trifacets.png Third stellation of cuboctahedron square facets.png
46 Fourth stellation of cuboctahedron Oh Fourth stellation of cuboctahedron.png Fourth stellation of cuboctahedron trifacets.png Fourth stellation of cuboctahedron square facets.png

Stellations of icosidodecahedron[edit]

Index Name Symmetry group Picture Facets (icosahedral planes) Facets (dodecahedral planes)
12 Icosidodecahedron
(regular)
Ih Zeroth stellation of icosidodecahedron.png Zeroth stellation of icosidodecahedron trifacets.png Zeroth stellation of icosidodecahedron pentfacets.png
47 (First stellation of icosidodecahedron)
Compound of dodecahedron and icosahedron
Ih First stellation of icosidodecahedron.png First stellation of icosidodecahedron facets.png First stellation of icosidodecahedron pentfacets.png
48 Second stellation of icosidodecahedron Ih Second stellation of icosidodecahedron.png Second stellation of icosidodecahedron facets.png Second stellation of icosidodecahedron pentfacets.png
49 Third stellation of icosidodecahedron Ih Third stellation of icosidodecahedron.png Third stellation of icosidodecahedron facets.png Third stellation of icosidodecahedron pentfacets.png
50 Fourth stellation of icosidodecahedron
(Compound of small stellated dodecahedron
and triakis icosahedron)
Ih Fourth stellation of icosidodecahedron.png Fourth stellation of icosidodecahedron facets.png Fourth stellation of icosidodecahedron pentfacets.png
51 Fifth stellation of icosidodecahedron
(Compound of small stellated dodecahedron
and five octahedra)
Ih Fifth stellation of icosidodecahedron.png Fifth stellation of icosidodecahedron facets.png Fifth stellation of icosidodecahedron pentfacets.png
52 Sixth stellation of icosidodecahedron Ih Sixth stellation of icosidodecahedron.png Sixth stellation of icosidodecahedron facets.png Sixth stellation of icosidodecahedron pentfacets.png
53 Seventh stellation of icosidodecahedron Ih Seventh stellation of icosidodecahedron.png Seventh stellation of icosidodecahedron facets.png Seventh stellation of icosidodecahedron pentfacets.png
54 Eighth stellation of icosidodecahedron
(Compound of five tetrahedra
and great dodecahedron)
I Eighth stellation of icosidodecahedron.png Eighth stellation of icosidodecahedron facets.png Eighth stellation of icosidodecahedron pentfacets.png
55 Ninth stellation of icosidodecahedron Ih Ninth stellation of icosidodecahedron.png Ninth stellation of icosidodecahedron facets.png Ninth stellation of icosidodecahedron pentfacets.png
56 Tenth stellation of icosidodecahedron Ih Tenth stellation of icosidodecahedron.png Tenth stellation of icosidodecahedron facets.png Tenth stellation of icosidodecahedron pentfacets.png
57 Eleventh stellation of icosidodecahedron Ih Eleventh stellation of icosidodecahedron.png Eleventh stellation of icosidodecahedron facets.png Eleventh stellation of icosidodecahedron pentfacets.png
58 Twelfth stellation of icosidodecahedron Ih Twelfth stellation of icosidodecahedron.png Twelfth stellation of icosidodecahedron facets.png Twelfth stellation of icosidodecahedron pentfacets.png
59 Thirteenth stellation of icosidodecahedron Ih Thirteenth stellation of icosidodecahedron.png Thirteenth stellation of icosidodecahedron facets.png Thirteenth stellation of icosidodecahedron pentfacets.png
60 Fourteenth stellation of icosidodecahedron Ih Fourteenth stellation of icosidodecahedron.png Fourteenth stellation of icosidodecahedron facets.png Fourteenth stellation of icosidodecahedron pentfacets.png
61 Compound of great stellated dodecahedron and great icosahedron Ih Second compound stellation of icosidecahedron.png Second compound stellation of icosidecahedron facets.png Second compound stellation of icosidecahedron pentfacets.png
62 Fifteenth stellation of icosidodecahedron Ih Fifteenth stellation of icosidodecahedron.png Fifteenth stellation of icosidodecahedron facets.png Fifteenth stellation of icosidodecahedron pentfacets.png
63 Sixteenth stellation of icosidodecahedron Ih Sixteenth stellation of icosidodecahedron.png Sixteenth stellation of icosidodecahedron facets.png Sixteenth stellation of icosidodecahedron pentfacets.png
64 Seventeenth stellation of icosidodecahedron Ih Seventeenth stellation of icosidodecahedron.png Seventeenth stellation of icosidodecahedron facets.png Seventeenth stellation of icosidodecahedron pentfacets.png
65 Eighteenth stellation of icosidodecahedron Ih Eighteenth stellation of icosidodecahedron.png Eighteenth stellation of icosidodecahedron facets.png Eighteenth stellation of icosidodecahedron pentfacets.png
66 Nineteenth stellation of icosidodecahedron Ih Nineteenth stellation of icosidodecahedron.png Nineteenth stellation of icosidodecahedron facets.png Nineteenth stellation of icosidodecahedron pentfacets.png

Uniform nonconvex solids W67 to W119[edit]

Index Name Picture Dual name Dual picture Wythoff symbol Vertex figure Symmetry group U# K# V E F Faces by type
67 Tetrahemihexahedron Tetrahemihexahedron.png Tetrahemihexacron Tetrahemihexacron.png 3/23|2 Tetrahemihexahedron vertfig.png
4.3/2.4.3
Td U04 K09 6 12 7 4{3}+3{4}
68 Octahemioctahedron Octahemioctahedron.png Octahemioctacron Hexahemioctacron.png 3/23|3 Octahemioctahedron vertfig.png
6.3/2.6.3
Oh U03 K08 12 24 12 8{3}+4{6}
69 Small cubicuboctahedron Small cubicuboctahedron.png Small hexacronic icositetrahedron DU13 small hexacronic icositetrahedron.png 3/24|4 Small cubicuboctahedron vertfig.png
8.3/2.8.4
Oh U13 K18 24 48 20 8{3}+6{4}+6{8}
70 Small ditrigonal icosidodecahedron Small ditrigonal icosidodecahedron.png Small triambic icosahedron DU30 small triambic icosahedron.png 3|5/23 Small ditrigonal icosidodecahedron vertfig.png
(5/2.3)3
Ih U30 K35 20 60 32 20{3}+12{5/2}
71 Small icosicosidodecahedron Small icosicosidodecahedron.png Small icosacronic hexecontahedron DU31 small icosacronic hexecontahedron.png 5/23|3 Small icosicosidodecahedron vertfig.png
6.5/2.6.3
Ih U31 K36 60 120 52 20{3}+12{5/2}+20{6}
72 Small dodecicosidodecahedron Small dodecicosidodecahedron.png Small dodecacronic hexecontahedron DU33 small dodecacronic hexecontahedron.png 3/25|5 Small dodecicosidodecahedron vertfig.png
10.3/2.10.5
Ih U33 K38 60 120 44 20{3}+12{5}+12{10}
73 Dodecadodecahedron Dodecadodecahedron.png Medial rhombic triacontahedron DU36 medial rhombic triacontahedron.png 2|5/25 Dodecadodecahedron vertfig.png
(5/2.5)2
Ih U36 K41 30 60 24 12{5}+12{5/2}
74 Small rhombidodecahedron Small rhombidodecahedron.png Small rhombidodecacron DU39 small rhombidodecacron.png 25/25| Small rhombidodecahedron vertfig.png
10.4.10/9.4/3
Ih U39 K44 60 120 42 30{4}+12{10}
75 Truncated great dodecahedron Great truncated dodecahedron.png Small stellapentakis dodecahedron DU37 small stellapentakisdodecahedron.png 25/2|5 Truncated great dodecahedron vertfig.png
10.10.5/2
Ih U37 K42 60 90 24 12{5/2}+12{10}
76 Rhombidodecadodecahedron Rhombidodecadodecahedron.png Medial deltoidal hexecontahedron DU38 medial trapezoidal hexecontahedron.png 5/25|2 Rhombidodecadodecahedron vertfig.png
4.5/2.4.5
Ih U38 K43 60 120 54 30{4}+12{5}+12{5/2}
77 Great cubicuboctahedron Great cubicuboctahedron.png Great hexacronic icositetrahedron DU14 great hexacronic icositetrahedron.png 3 4|4/3 Great cubicuboctahedron vertfig.png
8/3.3.8/3.4
Oh U14 K19 24 48 20 8{3}+6{4}+6{8/3}
78 Cubohemioctahedron Cubohemioctahedron.png Hexahemioctacron Hexahemioctacron.png 4/34|3 Cubohemioctahedron vertfig.png
6.4/3.6.4
Oh U15 K20 12 24 10 6{4}+4{6}
79 Cubitruncated cuboctahedron
(Cuboctatruncated cuboctahedron)
Cubitruncated cuboctahedron.png Tetradyakis hexahedron DU16 tetradyakishexahedron.png 4/33 4| Cubitruncated cuboctahedron vertfig.png
8/3.6.8
Oh U16 K21 48 72 20 8{6}+6{8}+6{8/3}
80 Ditrigonal dodecadodecahedron Ditrigonal dodecadodecahedron.png Medial triambic icosahedron DU41 medial triambic icosahedron.png 3|5/35 Ditrigonal dodecadodecahedron vertfig.png
(5/3.5)3
Ih U41 K46 20 60 24 12{5}+12{5/2
81 Great ditrigonal dodecicosidodecahedron Great ditrigonal dodecicosidodecahedron.png Great ditrigonal dodecacronic hexecontahedron DU42 great ditrigonal dodecacronic hexecontahedron.png 3 5|5/3 Great ditrigonal dodecicosidodecahedron vertfig.png
10/3.3.10/3.5
Ih U42 K47 60 120 44 20{3}+12{5}+12{10/3}
82 Small ditrigonal dodecicosidodecahedron Small ditrigonal dodecicosidodecahedron.png Small ditrigonal dodecacronic hexecontahedron DU43 Small ditrigonal dodecacronic hexecontahedron.png 5/33|5 Small ditrigonal dodecicosidodecahedron vertfig.png
10.5/3.10.3
Ih U43 K48 60 120 44 20{3}+12{5/2}+12{10}
83 Icosidodecadodecahedron Icosidodecadodecahedron.png Medial icosacronic hexecontahedron DU44 medial icosacronic hexecontahedron.png 5/35|3 Icosidodecadodecahedron vertfig.png
6.5/3.6.5
Ih U44 K49 60 120 44 12{5}+12{5/2}+20{6}
84 Icositruncated dodecadodecahedron
(Icosidodecatruncated icosidodecahedron)
Icositruncated dodecadodecahedron.png Tridyakis icosahedron DU45 tridyakisicosahedron.png 5/33 5| Icositruncated dodecadodecahedron vertfig.png
10/3.6.10
Ih U45 K50 120 180 44 20{6}+12{10}+12{10/3}
85 Nonconvex great rhombicuboctahedron
(Quasirhombicuboctahedron)
Uniform great rhombicuboctahedron.png Great deltoidal icositetrahedron DU17 great strombic icositetrahedron.png 3/24|2 Great rhombicuboctahedron vertfig.png
4.3/2.4.4
Oh U17 K22 24 48 26 8{3}+(6+12){4}
86 Small rhombihexahedron Small rhombihexahedron.png Small rhombihexacron DU18 small rhombihexacron.png 3/22 4| Small rhombihexahedron vertfig.png
4.8.4/3.8
Oh U18 K23 24 48 18 12{4}+6{8}
87 Great ditrigonal icosidodecahedron Great ditrigonal icosidodecahedron.png Great triambic icosahedron DU47 great triambic icosahedron.png 3/2|3 5 Great ditrigonal icosidodecahedron vertfig.png
(5.3.5.3.5.3)/2
Ih U47 K52 20 60 32 20{3}+12{5}
88 Great icosicosidodecahedron Great icosicosidodecahedron.png Great icosacronic hexecontahedron DU48 great icosacronic hexecontahedron.png 3/25|3 Great icosicosidodecahedron vertfig.png
6.3/2.6.5
Ih U48 K53 60 120 52 20{3}+12{5}+20{6}
89 Small icosihemidodecahedron Small icosihemidodecahedron.png Small icosihemidodecacron Small dodecahemidodecacron.png 3/23|5 Small icosihemidodecahedron vertfig.png
10.3/2.10.3
Ih U49 K54 30 60 26 20{3}+6{10}
90 Small dodecicosahedron Small dodecicosahedron.png Small dodecicosacron DU50 small dodecicosacron.png 3/23 5| Small dodecicosahedron vertfig.png
10.6.10/9.6/5
Ih U50 K55 60 120 32 20{6}+12{10}
91 Small dodecahemidodecahedron Small dodecahemidodecahedron.png Small dodecahemidodecacron Small dodecahemidodecacron.png 5/45|5 Small dodecahemidodecahedron vertfig.png
10.5/4.10.5
Ih U51 K56 30 60 18 12{5}+6{10}
92 Stellated truncated hexahedron
(Quasitruncated hexahedron)
Stellated truncated hexahedron.png Great triakis octahedron DU19 great triakisoctahedron.png 2 3|4/3 Stellated truncated hexahedron vertfig.png
8/3.8/3.3
Oh U19 K24 24 36 14 8{3}+6{8/3}
93 Great truncated cuboctahedron
(Quasitruncated cuboctahedron)
Great truncated cuboctahedron.png Great disdyakis dodecahedron DU20 great disdyakisdodecahedron.png 4/32 3| Great truncated cuboctahedron vertfig.png
8/3.4.6
Oh U20 K25 48 72 26 12{4}+8{6}+6{8/3}
94 Great icosidodecahedron Great icosidodecahedron.png Great rhombic triacontahedron DU54 great rhombic triacontahedron.png 2|5/23 Great icosidodecahedron vertfig.png
(5/2.3)2
Ih U54 K59 30 60 32 20{3}+12{5/2}
95 Truncated great icosahedron Great truncated icosahedron.png Great stellapentakis dodecahedron DU55 great stellapentakisdodecahedron.png 25/2|3 Great truncated icosahedron vertfig.png
6.6.5/2
Ih U55 K60 60 90 32 12{5/2}+20{6}
96 Rhombicosahedron Rhombicosahedron.png Rhombicosacron DU56 rhombicosacron.png 25/23| Rhombicosahedron vertfig.png
6.4.6/5.4/3
Ih U56 K61 60 120 50 30{4}+20{6}
97 Small stellated truncated dodecahedron
(Quasitruncated small stellated dodecahedron)
Small stellated truncated dodecahedron.png Great pentakis dodecahedron DU58 great pentakisdodecahedron.png 2 5|5/3 Small stellated truncated dodecahedron vertfig.png
10/3.10/3.5
Ih U58 K63 60 90 24 12{5}+12{10/3}
98 Truncated dodecadodecahedron
(Quasitruncated dodecahedron)
Truncated dodecadodecahedron.png Medial disdyakis triacontahedron DU59 medial disdyakistriacontahedron.png 5/32 5| Truncated dodecadodecahedron vertfig.png
10/3.4.10
Ih U59 K64 120 180 54 30{4}+12{10}+12{10/3}
99 Great dodecicosidodecahedron Great dodecicosidodecahedron.png Great dodecacronic hexecontahedron DU61 great dodecacronic hexecontahedron.png 5/23|5/3 Great dodecicosidodecahedron vertfig.png
10/3.5/2.10/3.3
Ih U61 K66 60 120 44 20{3}+12{5/2}+12{10/3 }
100 Small dodecahemicosahedron Small dodecahemicosahedron.png Small dodecahemicosacron Small dodecahemicosacron.png 5/35/2|3 Small dodecahemicosahedron vertfig.png
6.5/3.6.5/2
Ih U62 K67 30 60 22 12{5/2}+10{6}
101 Great dodecicosahedron Great dodecicosahedron.png Great dodecicosacron DU63 great dodecicosacron.png 5/35/23| Great dodecicosahedron vertfig.png
6.10/3.6/5.10/7
Ih U63 K68 60 120 32 20{6}+12{10/3}
102 Great dodecahemicosahedron Great dodecahemicosahedron.png Great dodecahemicosacron Small dodecahemicosacron.png 5/45|3 Great dodecahemicosahedron vertfig.png
6.5/4.6.5
Ih U65 K70 30 60 22 12{5}+10{6}
103 Great rhombihexahedron Great rhombihexahedron.png Great rhombihexacron DU21 great rhombihexacron.png 4/33/22| Great rhombihexahedron vertfig.png
4.8/3.4/3.8/5
Oh U21 K26 24 48 18 12{4}+6{8/3}
104 Great stellated truncated dodecahedron
(Quasitruncated great stellated dodecahedron)
Great stellated truncated dodecahedron.png Great triakis icosahedron DU66 great triakisicosahedron.png 2 3|5/3 Great stellated truncated dodecahedron vertfig.png
10/3.10/3.3
Ih U66 K71 60 90 32 20{3}+12{10/3}
105 Nonconvex great rhombicosidodecahedron
(Quasirhombicosidodecahedron)
Uniform great rhombicosidodecahedron.png Great deltoidal hexecontahedron DU67 great strombic hexecontahedron.png 5/33|2 Uniform great rhombicosidodecahedron vertfig.png
4.5/3.4.3
Ih U67 K72 60 120 62 20{3}+30{4}+12{5/2}
106 Great icosihemidodecahedron Great icosihemidodecahedron.png Great icosihemidodecacron Great dodecahemidodecacron.png 3 3|5/3 Great icosihemidodecahedron vertfig.png
10/3.3/2.10/3.3
Ih U71 K76 30 60 26 20{3}+6{10/3}
107 Great dodecahemidodecahedron Great dodecahemidodecahedron.png Great dodecahemidodecacron Great dodecahemidodecacron.png 5/35/2|5/3 Great dodecahemidodecahedron vertfig.png
10/3.5/3.10/3.5/2
Ih U70 K75 30 60 18 12{5/2}+6{10/3}
108 Great truncated icosidodecahedron
(Great quasitruncated icosidodecahedron)
Great truncated icosidodecahedron.png Great disdyakis triacontahedron DU68 great disdyakistriacontahedron.png 5/32 3| Great truncated icosidodecahedron vertfig.png
10/3.4.6
Ih U68 K73 120 180 62 30{4}+20{6}+12{10/3}
109 Great rhombidodecahedron Great rhombidodecahedron.png Great rhombidodecacron DU73 great rhombidodecacron.png 3/25/32| Great rhombidodecahedron vertfig.png
4.10/3.4/3.10/7
Ih U73 K78 60 120 42 30{4}+12{10/3}
110 Small snub icosicosidodecahedron Small snub icosicosidodecahedron.png Small hexagonal hexecontahedron DU32 small hexagonal hexecontahedron.png |5/23 3 Small snub icosicosidodecahedron vertfig.png
3.3.3.3.3.5/2
Ih U32 K37 60 180 112 (40+60){3}+12{5/2}
111 Snub dodecadodecahedron Snub dodecadodecahedron.png Medial pentagonal hexecontahedron DU40 medial pentagonal hexecontahedron.png |25/25 Snub dodecadodecahedron vertfig.png
3.3.5/2.3.5
I U40 K45 60 150 84 60{3}+12{5}+12{5/2}
112 Snub icosidodecadodecahedron Snub icosidodecadodecahedron.png Medial hexagonal hexecontahedron DU46 medial hexagonal hexecontahedron.png |5/33 5 Snub icosidodecadodecahedron vertfig.png
3.3.3.3.5.5/3
I U46 K51 60 180 104 (20+6){3}+12{5}+12{5/2}
113 Great inverted snub icosidodecahedron Great inverted snub icosidodecahedron.png Great inverted pentagonal hexecontahedron DU69 great inverted pentagonal hexecontahedron.png |5/32 3 Great inverted snub icosidodecahedron vertfig.png
3.3.3.3.5/3
I U69 K74 60 150 92 (20+60){3}+12{5/2}
114 Inverted snub dodecadodecahedron Inverted snub dodecadodecahedron.png Medial inverted pentagonal hexecontahedron DU60 medial inverted pentagonal hexecontahedron.png |5/32 5 Inverted snub dodecadodecahedron vertfig.png
3.5/3.3.3.5
I U60 K65 60 150 84 60{3}+12{5}+12{5/2}
115 Great snub dodecicosidodecahedron Great snub dodecicosidodecahedron.png Great hexagonal hexecontahedron DU64 great hexagonal hexecontahedron.png |5/35/23 Great snub dodecicosidodecahedron vertfig.png
3.5/3.3.5/2.3.3
I U64 K69 60 180 104 (20+60){3}+(12+12){5/2}
116 Great snub icosidodecahedron Great snub icosidodecahedron.png Great pentagonal hexecontahedron DU57 great pentagonal hexecontahedron (2).png |25/25/2 Great snub icosidodecahedron vertfig.png
3.3.3.3.5/2
I U57 K62 60 150 92 (20+60){3}+12{5/2}
117 Great retrosnub icosidodecahedron Great retrosnub icosidodecahedron.png Great pentagrammic hexecontahedron DU74 great pentagrammic hexecontahedron.png |3/25/32 Great retrosnub icosidodecahedron vertfig.png
(3.3.3.3.5/3)/2
I U74 K79 60 150 92 (20+60){3}+12{5/2}
118 Small retrosnub icosicosidodecahedron Small retrosnub icosicosidodecahedron.png Small hexagrammic hexecontahedron DU72 small hexagrammic hexecontahedron.png |3/23/25/2 Small retrosnub icosicosidodecahedron vertfig.png
(3.3.3.3.3.5/2)/2
Ih U72 K77 180 60 112 (40+60){3}+12{5/2}
119 Great dirhombicosidodecahedron Great dirhombicosidodecahedron.png Great dirhombicosidodecacron Great dirhombicosidodecacron.png |3/25/335/2 Great dirhombicosidodecahedron vertfig.png
(4.5/3.4.3.4.5/2.4.3/2)/2
Ih U75 K80 60 240 124 40{3}+60{4}+24{5/2}

See also[edit]

References[edit]

External links[edit]