List of Wenninger polyhedron models#Stellations: models W19 to W66
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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
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! Index ! Name ! Picture ! Dual name ! Dual picture ! Vertex figure ! Symmetry group ! U# ! K# ! V ! E ! F ! Faces by type |
1
| 80px | 80px | 3{{pipe}}2 3 | 80px | Td | U01 | K06 | 4 | 6 | 4 | 4{3} |
2
| 80px | 80px | 4{{pipe}}2 3 | 80px | Oh | U05 | K10 | 6 | 12 | 8 | 8{3} |
3
| Hexahedron (Cube) | 80px | 80px | 3{{pipe}}2 4 | 80px | Oh | U06 | K11 | 8 | 12 | 6 | 6{4} |
4
| 80px | 80px | 5{{pipe}}2 3 | 80px | Ih | U22 | K27 | 12 | 30 | 20 | 20{3} |
5
| 80px | 80px | 3{{pipe}}2 5 | 80px | Ih | U23 | K28 | 20 | 30 | 12 | 12{5} |
[[Archimedean solids]] (Semiregular) W6 to W18
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! Index ! Name ! Picture ! Dual name ! Dual picture ! Symmetry group ! U# ! K# ! V ! E ! F ! Faces by type | |
6
| 80px | File:triakis tetrahedron.png
| 2 3{{pipe}}3 | 80px | Td | U02 | K07 | 12 | 18 | 8 | 4{3} + 4{6} |
7
| 80px | File:tetrakis cube.png
| 2 4{{pipe}}3 | 80px | Oh | U08 | K13 | 14 | 36 | 24 | 6{4} + 8{6} |
8
| 80px | File:triakis octahedron.png
| 2 3{{pipe}}4 | 80px | Oh | U09 | K14 | 24 | 36 | 14 | 8{3} + 6{8} |
9
| 80px | File:pentakis dodecahedron.png
| 2 5{{pipe}}3 | 80px | Ih | U25 | K30 | 60 | 90 | 32 | 12{5} + 20{6} |
10
| 80px | File:triakis icosahedron.png
| 2 3{{pipe}}5 | 80px | Ih | U26 | K31 | 60 | 90 | 32 | 20{3} + 12{10} |
11
| 80px | File:rhombic dodecahedron.png
| 2{{pipe}}3 4 | 80px | Oh | U07 | K12 | 12 | 24 | 14 | 8{3} + 6{4} |
12
| 80px | File:rhombic triacontahedron.png
| 2{{pipe}}3 5 | 80px | Ih | U24 | K29 | 30 | 60 | 32 | 20{3} + 12{5} |
13
| 80px | File:Strombic icositetrahedron.png
| 3 4{{pipe}}2 | 80px | Oh | U10 | K15 | 24 | 48 | 26 | 8{3}+(6+12){4} |
14
| Small rhombicosidodecahedron | 80px | File:Strombic hexecontahedron.png
| 3 5{{pipe}}2 | 80px | Ih | U27 | K32 | 60 | 120 | 62 | 20{3} + 30{4} + 12{5} |
15
| Truncated cuboctahedron | 80px | File:disdyakis dodecahedron.png
| 2 3 4{{pipe}} | 80px | Oh | U11 | K16 | 48 | 72 | 26 | 12{4} + 8{6} + 6{8} |
16
| Truncated icosidodecahedron |80px | File:disdyakis triacontahedron.png
| 2 3 5{{pipe}} | 80px | Ih | U28 | K33 | 120 | 180 | 62 | 30{4} + 20{6} + 12{10} |
17
| 80px | File:pentagonal icositetrahedron.png
| {{pipe}}2 3 4 | 80px | O | U12 | K17 | 24 | 60 | 38 | (8 + 24){3} + 6{4} |
18
| 80px | File:Pentagonal hexecontahedron.png
| {{pipe}}2 3 5 | 80px | I | U29 | K34 | 60 | 150 | 92 | (20 + 60){3} + 12{5} |
[[Kepler–Poinsot polyhedra]] (Regular [[Star polyhedron|star polyhedra]]) W20, W21, W22 and W41
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! Index ! Name ! Picture ! Dual name ! Dual picture ! Vertex figure ! Symmetry group ! U# ! K# ! V ! E ! F ! Faces by type |
20
| Small stellated dodecahedron | 80px | 80px | 5{{pipe}}25/2 | 80px | Ih | U34 | K39 | 12 | 30 | 12 | 12{5/2} |
21
| 80px | Small stellated dodecahedron | 80px | 5/2{{pipe}}2 5 | 80px | Ih | U35 | K40 | 12 | 30 | 12 | 12{5} |
22
| Great stellated dodecahedron | 80px | 80px | 3{{pipe}}25/2 | 80px | Ih | U52 | K57 | 20 | 30 | 12 | 12{5/2} |
41
| Great icosahedron | 80px | Great stellated dodecahedron | 80px | 5/2{{pipe}}2 3 | 80px | Ih | U53 | K58 | 12 | 30 | 20 | 20{3} |
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Stellations: models W19 to W66
=Stellations of octahedron=
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! Index ! Name ! Symmetry group ! Picture ! Facets |
2
| Octahedron | Oh | 100px | 100px |
19
| Stellated octahedron | Oh | 100px | 100px |
===Stellations of dodecahedron===
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! Index ! Name ! Symmetry group ! Picture ! Facets |
5
| Dodecahedron (regular) | Ih | 100px | 100px |
20
| Small stellated dodecahedron (regular) | Ih | 100px | 100px |
21
| Great dodecahedron (regular) | Ih | 100px | 100px |
22
| Great stellated dodecahedron (regular) | Ih | 100px | 100px |
=Stellations of icosahedron=
=Stellations of cuboctahedron=
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! Index ! Name ! Symmetry group ! Picture ! Facets (octahedral planes) ! Facets (cube planes) |
11
| Cuboctahedron (regular) | Oh | 100px | 100px | 100px |
43
| Compound of cube and octahedron | Oh | 100px | 100px | 100px |
44
| Second stellation of cuboctahedron | Oh | 100px | 100px | 100px |
45
| Third stellation of cuboctahedron | Oh | 100px | 100px | 100px |
46
| Fourth stellation of cuboctahedron | Oh | 100px | 100px | 100px |
===Stellations of icosidodecahedron===
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Uniform nonconvex solids W67 to W119
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See also
References
- {{cite book | first=Magnus | last=Wenninger | authorlink=Magnus Wenninger | title=Polyhedron Models | publisher=Cambridge University Press | year=1974 | isbn=0-521-09859-9 }}
- Errata
- In Wenninger, the vertex figure for W90 is incorrectly shown as having parallel edges.
- {{cite book | first=Magnus | last=Wenninger | authorlink=Magnus Wenninger | title=Spherical Models | url=https://archive.org/details/sphericalmodels0000wenn | url-access=registration | publisher=Cambridge University Press | year=1979 | isbn=0-521-29432-0 }}
External links
- [https://web.archive.org/web/20051001035323/http://www.employees.csbsju.edu/mwenninger/ Magnus J. Wenninger]
- Software used to generate images in this article:
- [http://www.software3d.com/Stella.php Stella: Polyhedron Navigator] Stella (software) - Can create and print nets for all of Wenninger's polyhedron models.
- [http://bulatov.org/polyhedra/stellation_applet Vladimir Bulatov's Polyhedra Stellations Applet]
- [http://davidcool.com/Stellation.zip Vladimir Bulatov's Polyhedra Stellations Applet packaged as an OS X application] {{Webarchive|url=https://web.archive.org/web/20160304025232/http://davidcool.com/Stellation.zip |date=2016-03-04 }}
- [http://www.steelpillow.com/polyhedra/Wenninger/Wenninger.html M. Wenninger, Polyhedron Models, Errata]: known errors in the various editions.
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