User:Pfafrich/test
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[edit] Using switch
8
tetra Faces: 4 Edges: Vertices:
[edit] Using callback one template per poly
Tetrahedron Faces: 4 Edges: 6 Vertices: 4
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| Name | Image | Vertex Figure | Wythoff | Vertices | Edges | Faces | Chi | Group | References |
|---|---|---|---|---|---|---|---|---|---|
| Tetrahedron |
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 3.3.3 |
3|3 2 | 4 | 6 | 4=4{3} | 2 | Td | W1, U01, K06, C15 |
| Octahedron |
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 3.3.3.3 |
4|3 2 | 6 | 12 | 8=8{3} | 2 | Oh | W2, U05, K10, C17 |
| Cube (Hexahedron) |
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 4.4.4 |
3|4 2 | 8 | 12 | 6=6{4} | 2 | Oh | W3, U06, K11, C18 |
| Icosahedron |
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 3.3.3.3.3 |
5|3 2 | 12 | 30 | 20=20{3} | 2 | Ih | W4, U22, K27, C25 |
| Dodecahedron |
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 5.5.5 |
3|5 2 | 20 | 30 | 12=12{5} | 2 | Ih | W5, U23, K28, C26 |
[edit] Using callback with database of properties
[edit] Regular
All the faces are identical, each edge is identical and each vertex is identical. The all have a Wythoff symbol of the form p|q r, and at one of q or r is 2.
[edit] Convex
The Platoid solids.
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[edit] Non-convex
The Kepler Posisot solids.
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[edit] Quasi-regular
Each edge is identical and each vertex is identical. There are two types of faces which apear in an alternating fashon around each vertex. The first row are semi-regular with 4 faces around each vertex. They fave Wythoff symbol 2|p q. The second row are ditriogonal with 6 faces around each vertex. They have Wythoff symbol 3|p q or 3/2|p q.
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[edit] Truncated regular forms
Each vertex has three faces surronding it, two of which are identical. These all have Wythoff symbols 2 p|q, some are constructed by truncating the regular soilds.
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[edit] Hemi-hedra
The hemi-hedra all have faces which pass through the origin. Their Wythoff symbols are of the form p p/m|q or p/m p/n|q. With the exception of the tetrahemihexahedron they occur in pairs, and are closely related to the semi-regular polyhedra, like the cuboctohedron.
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[edit] Rhombic quais-regular
Four faces around the vertex in the pattern p.q.r.q. The name rhombic stems from inserting a square in the cubeoctohedron and icodocehedron. The Wythoff symbol is of the form p q|r.
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[edit] Other truncated forms
These have three different faces around each vertex, and the verticies do not lie on any plane of symetry. The have Wythoff symbol p q r|.
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[edit] quasi-rhombic
Vertex pattern p.q.r.q. Wythoff p q r|.
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