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 (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 convex polyhedra) W1 to W5
Index Name Picture Dual name Dual picture Wythoff symbol Vertex figureand Schläfli symbol Symmetry group U# K# V E F Faces by type 1 Tetrahedron Tetrahedron 32 3 {3,3} Td U01 K06 4 6 4 4{3} 2 Octahedron Hexahedron 42 3 {3,4} Oh U05 K10 6 12 8 8{3} 3 Hexahedron (Cube) Octahedron 32 4 {4,3} Oh U06 K11 8 12 6 6{4} 4 Icosahedron Dodecahedron 52 3 {3,5} Ih U22 K27 12 30 20 20{3} 5 Dodecahedron Icosahedron 32 5 {5,3} Ih U23 K28 20 30 12 12{5}
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 33 3.6.6 Td U02 K07 12 18 8 4{3} + 4{6} 7 Truncated octahedron tetrakis hexahedron 2 43 4.6.6 Oh U08 K13 14 36 24 6{4} + 8{6} 8 Truncated hexahedron triakis octahedron 2 34 3.8.8 Oh U09 K14 24 36 14 8{3} + 6{8} 9 Truncated icosahedron pentakis dodecahedron 2 53 5.6.6 Ih U25 K30 60 90 32 12{5} + 20{6} 10 Truncated dodecahedron triakis icosahedron 2 35 3.10.10 Ih U26 K31 60 90 32 20{3} + 12{10} 11 Cuboctahedron rhombic dodecahedron 23 4 3.4.3.4 Oh U07 K12 12 24 14 8{3} + 6{4} 12 Icosidodecahedron rhombic triacontahedron 23 5 3.5.3.5 Ih U24 K29 30 60 32 20{3} + 12{5} 13 Small rhombicuboctahedron deltoidal icositetrahedron 3 42 3.4.4.4 Oh U10 K15 24 48 26 8{3}+(6+12){4} 14 Small rhombicosidodecahedron deltoidal hexecontahedron 3 52 3.4.5.4 Ih U27 K32 60 120 62 20{3} + 30{4} + 12{5} 15 Truncated cuboctahedron(Great rhombicuboctahedron) disdyakis dodecahedron 2 3 4 4.6.8 Oh U11 K16 48 72 26 12{4} + 8{6} + 6{8} 16 Truncated icosidodecahedron(Great rhombicosidodecahedron) disdyakis triacontahedron 2 3 5 4.6.10 Ih U28 K33 120 180 62 30{4} + 20{6} + 12{10} 17 Snub cube pentagonal icositetrahedron 2 3 4 3.3.3.3.4 O U12 K17 24 60 38 (8 + 24){3} + 6{4} 18 Snub dodecahedron pentagonal hexecontahedron 2 3 5 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
Index Name Picture Dual name Dual picture Wythoff symbol Vertex figureand Schläfli symbol Symmetry group U# K# V E F Faces by type 20 Small stellated dodecahedron Great dodecahedron 525/2 {5/2,5} Ih U34 K39 12 30 12 12{5/2} 21 Great dodecahedron Small stellated dodecahedron 5/22 5 {5,5/2} Ih U35 K40 12 30 12 12{5} 22 Great stellated dodecahedron Great icosahedron 325/2 {5/2,3} Ih U52 K57 20 30 12 12{5/2} 41 Great icosahedron(16th stellation of icosahedron) Great stellated dodecahedron 5/22 3 {3,5/2} Ih U53 K58 12 30 20 20{3}
Stellations: models W19 to W66
Stellations of octahedron Index Name Symmetry group Picture Facets 2 Octahedron(regular) Oh 19 Stellated octahedron(Compound of two tetrahedra) Oh
Stellations of dodecahedron Index Name Symmetry group Picture Facets 5 Dodecahedron (regular) Ih 20 Small stellated dodecahedron (regular)(First stellation of dodecahedron) Ih 21 Great dodecahedron (regular)(Second stellation of dodecahedron) Ih 22 Great stellated dodecahedron (regular)(Third stellation of dodecahedron) Ih
Stellations of icosahedron Index Name Symmetry group Picture Facets 4 Icosahedron (regular) Ih 23 Compound of five octahedra(First compound stellation of icosahedron) Ih 24 Compound of five tetrahedra(Second compound stellation of icosahedron) I 25 Compound of ten tetrahedra(Third compound stellation of icosahedron) Ih 26 Small triambic icosahedron(First stellation of icosahedron)(Triakis icosahedron) Ih 27 Second stellation of icosahedron Ih 28 Excavated dodecahedron(Third stellation of icosahedron) Ih 29 Fourth stellation of icosahedron Ih 30 Fifth stellation of icosahedron Ih 31 Sixth stellation of icosahedron Ih 32 Seventh stellation of icosahedron Ih 33 Eighth stellation of icosahedron Ih 34 Ninth stellation of icosahedronGreat triambic icosahedron Ih 35 Tenth stellation of icosahedron I 36 Eleventh stellation of icosahedron I 37 Twelfth stellation of icosahedron Ih 38 Thirteenth stellation of icosahedron I 39 Fourteenth stellation of icosahedron I 40 Fifteenth stellation of icosahedron I 41 Great icosahedron (regular)(Sixteenth stellation of icosahedron) Ih 42 Final stellation of the icosahedron Ih
Stellations of cuboctahedron Index Name Symmetry group Picture Facets (octahedral planes) Facets (cube planes) 11 Cuboctahedron (regular) Oh 43 Compound of cube and octahedron(First stellation of cuboctahedron) Oh 44 Second stellation of cuboctahedron Oh 45 Third stellation of cuboctahedron Oh 46 Fourth stellation of cuboctahedron Oh
Stellations of icosidodecahedron Index Name Symmetry group Picture Facets (icosahedral planes) Facets (dodecahedral planes) 12 Icosidodecahedron(regular) Ih 47 (First stellation of icosidodecahedron)Compound of dodecahedron and icosahedron Ih 48 Second stellation of icosidodecahedron Ih 49 Third stellation of icosidodecahedron Ih 50 Fourth stellation of icosidodecahedron(Compound of small stellated dodecahedronand triakis icosahedron) Ih 51 Fifth stellation of icosidodecahedron(Compound of small stellated dodecahedronand five octahedra) Ih 52 Sixth stellation of icosidodecahedron Ih 53 Seventh stellation of icosidodecahedron Ih 54 Eighth stellation of icosidodecahedron(Compound of five tetrahedraand great dodecahedron) I 55 Ninth stellation of icosidodecahedron Ih 56 Tenth stellation of icosidodecahedron Ih 57 Eleventh stellation of icosidodecahedron Ih 58 Twelfth stellation of icosidodecahedron Ih 59 Thirteenth stellation of icosidodecahedron Ih 60 Fourteenth stellation of icosidodecahedron Ih 61 Compound of great stellated dodecahedron and great icosahedron Ih 62 Fifteenth stellation of icosidodecahedron Ih 63 Sixteenth stellation of icosidodecahedron Ih 64 Seventeenth stellation of icosidodecahedron Ih 65 Eighteenth stellation of icosidodecahedron Ih 66 Nineteenth stellation of icosidodecahedron Ih
Uniform nonconvex solids W67 to W119