Small stellapentakis dodecahedron
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Small stellapentakis dodecahedron | |
---|---|
Rank | 3 |
Type | Uniform dual |
Notation | |
Coxeter diagram | o5/2m5m () |
Elements | |
Faces | 60 isosceles triangles |
Edges | 30+60 |
Vertices | 12+12 |
Vertex figure | 12 pentagrams, 12 decagons |
Measures (edge length 1) | |
Inradius | |
Dihedral angle | |
Central density | 3 |
Number of external pieces | 120 |
Related polytopes | |
Dual | Truncated great dodecahedron |
Conjugate | Great pentakis dodecahedron |
Convex core | Non-Catalan pentakis dodecahedron |
Abstract & topological properties | |
Flag count | 360 |
Euler characteristic | –6 |
Orientable | Yes |
Genus | 4 |
Properties | |
Symmetry | H3, order 120 |
Convex | No |
Nature | Tame |
The small stellapentakis dodecahedron is a uniform dual polyhedron. It consists of 60 isosceles triangles.
If its dual, the truncated great dodecahedron, has an edge length of 1, then the side edges of the triangles will measure , and the base edges will be . The triangles have two interior angles of , and one of .
Vertex coordinates[edit | edit source]
A small stellapentakis dodecahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
- ,
- .
External links[edit | edit source]
- Wikipedia contributors. "Small stellapentakis dodecahedron".
- McCooey, David. "Small Stellapentakis Dodecahedron"