List of Wenninger polyhedron models
This is 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.
Models listed here can be cited as "Wenninger Model Number N", or WN for brevity.
The polyhedra are grouped in 5 tables: Regular, Semiregular, regular star polyhedra, Stellations and compounds, and uniform star polyhedra. 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
| 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 | 3|2 3 | Td | U01 | K06 | 4 | 6 | 4 | 4 | |||
| 2 | Octahedron | Hexahedron | 4|2 3 | Oh | U05 | K10 | 6 | 12 | 8 | 8 | |||
| 3 | Hexahedron | Octahedron | 3|2 4 | Oh | U06 | K11 | 8 | 12 | 6 | 6 | |||
| 4 | Icosahedron | Dodecahedron | 5|2 3 | Ih | U22 | K27 | 12 | 30 | 20 | 20 | |||
| 5 | Dodecahedron | Icosahedron | 3|2 5 | Ih | U23 | K28 | 20 | 30 | 12 | 12 |
[Archimedean solids] (Semiregular) W6 to W18
| Index | Name | Picture | Dual name | Dual picture | Wythoff symbol | Vertex figure | Symmetry group | U# | K# | V | E | F | Faces by type |
| 6 | Truncated tetrahedron | triakis tetrahedron | 2 3|3 | 3.6.6 | Td | U02 | K07 | 12 | 18 | 8 | 4 + 4 | ||
| 7 | Truncated octahedron | tetrakis hexahedron | 2 4|3 | 4.6.6 | Oh | U08 | K13 | 24 | 36 | 24 | 6 + 8 | ||
| 8 | Truncated hexahedron | triakis octahedron | 2 3|4 | 3.8.8 | Oh | U09 | K14 | 24 | 36 | 14 | 8 + 6 | ||
| 9 | Truncated icosahedron | pentakis dodecahedron | 2 5|3 | 5.6.6 | Ih | U25 | K30 | 60 | 90 | 32 | 12 + 20 | ||
| 10 | Truncated dodecahedron | triakis icosahedron | 2 3|5 | 3.10.10 | Ih | U26 | K31 | 60 | 90 | 32 | 20 + 12 | ||
| 11 | Cuboctahedron | rhombic dodecahedron | 2|3 4 | 3.4.3.4 | Oh | U07 | K12 | 12 | 24 | 14 | 8 + 6 | ||
| 12 | Icosidodecahedron | rhombic triacontahedron | 2|3 5 | 3.5.3.5 | Ih | U24 | K29 | 30 | 60 | 32 | 20 + 12 | ||
| 13 | Small rhombicuboctahedron | deltoidal icositetrahedron | 3 4|2 | 3.4.4.4 | Oh | U10 | K15 | 24 | 48 | 26 | 8+ | ||
| 14 | Small rhombicosidodecahedron | deltoidal hexecontahedron | 3 5|2 | 3.4.5.4 | Ih | U27 | K32 | 60 | 120 | 62 | 20 + 30 + 12 | ||
| 15 | Truncated cuboctahedron | disdyakis dodecahedron | 2 3 4| | 4.6.8 | Oh | U11 | K16 | 48 | 72 | 26 | 12 + 8 + 6 | ||
| 16 | Truncated icosidodecahedron | disdyakis triacontahedron | 2 3 5| | 4.6.10 | Ih | U28 | K33 | 120 | 180 | 62 | 30 + 20 + 12 | ||
| 17 | Snub cube | pentagonal icositetrahedron | |2 3 4 | 3.3.3.3.4 | O | U12 | K17 | 24 | 60 | 38 | + 6 | ||
| 18 | Snub dodecahedron | pentagonal hexecontahedron | |2 3 5 | 3.3.3.3.5 | I | U29 | K34 | 60 | 150 | 92 | + 12 |
[Kepler–Poinsot polyhedra] (Regular star polyhedra">Star polyhedron">star polyhedra) W20, W21, W22 and W41
| 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 | Great dodecahedron | 5|25/2 | Ih | U34 | K39 | 12 | 30 | 12 | 12 | |||
| 21 | Great dodecahedron | Small stellated dodecahedron | 5/2|2 5 | Ih | U35 | K40 | 12 | 30 | 12 | 12 | |||
| 22 | Great stellated dodecahedron | Great icosahedron | 3|25/2 | Ih | U52 | K57 | 20 | 30 | 12 | 12 | |||
| 41 | Great icosahedron | Great stellated dodecahedron | 5/2|2 3 | Ih | U53 | K58 | 12 | 30 | 20 | 20 |