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 convex polyhedra) W1 to W5

IndexNamePictureDual nameDual pictureWythoff symbolVertex figure
and Schläfli symbol
Symmetry groupU#K#VEFFaces by type
1TetrahedronTetrahedron32 3
TdU01K064644
2OctahedronHexahedron42 3
OhU05K1061288
3Hexahedron Octahedron32 4
OhU06K1181266
4IcosahedronDodecahedron52 3
IhU22K2712302020
5DodecahedronIcosahedron32 5
IhU23K2820301212

[Archimedean solids] (Semiregular) W6 to W18

IndexNamePictureDual nameDual pictureWythoff symbolVertex figureSymmetry groupU#K#VEFFaces by type
6Truncated tetrahedrontriakis tetrahedron2 33
3.6.6
TdU02K07121884 + 4
7Truncated octahedrontetrakis hexahedron2 43
4.6.6
OhU08K131436246 + 8
8Truncated hexahedrontriakis octahedron2 34
3.8.8
OhU09K142436148 + 6
9Truncated icosahedronpentakis dodecahedron2 53
5.6.6
IhU25K3060903212 + 20
10Truncated dodecahedrontriakis icosahedron2 35
3.10.10
IhU26K3160903220 + 12
11Cuboctahedronrhombic dodecahedron23 4
3.4.3.4
OhU07K121224148 + 6
12Icosidodecahedronrhombic triacontahedron23 5
3.5.3.5
IhU24K2930603220 + 12
13Small rhombicuboctahedrondeltoidal icositetrahedron3 42
3.4.4.4
OhU10K152448268+
14Small rhombicosidodecahedrondeltoidal hexecontahedron3 52
3.4.5.4
IhU27K32601206220 + 30 + 12
15Truncated cuboctahedron
disdyakis dodecahedron2 3 4
4.6.8
OhU11K1648722612 + 8 + 6
16Truncated icosidodecahedron
disdyakis triacontahedron2 3 5
4.6.10
IhU28K331201806230 + 20 + 12
17Snub cubepentagonal icositetrahedron2 3 4
3.3.3.3.4
OU12K17246038 + 6
18Snub dodecahedronpentagonal hexecontahedron2 3 5
3.3.3.3.5
IU29K346015092 + 12

[Kepler–Poinsot polyhedra] (Regular star polyhedra">Star polyhedron">star polyhedra) W20, W21, W22 and W41

IndexNamePictureDual nameDual pictureWythoff symbolVertex figure
and Schläfli symbol
Symmetry groupU#K#VEFFaces by type
20Small stellated dodecahedronGreat dodecahedron525/2
IhU34K3912301212
21Great dodecahedronSmall stellated dodecahedron5/22 5
IhU35K4012301212
22Great stellated dodecahedronGreat icosahedron325/2
IhU52K5720301212
41Great icosahedron
Great stellated dodecahedron5/22 3
IhU53K5812302020