Small dodecahemidodecahedron
Appearance
Small dodecahemidodecahedron | |
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![]() | |
Type | Uniform star polyhedron |
Elements | F = 18, E = 60 V = 30 (χ = −12) |
Faces by sides | 12{5}+6{10} |
Coxeter diagram | ![]() ![]() ![]() ![]() |
Wythoff symbol | 5/4 5 | 5 (double covering) |
Symmetry group | Ih, [5,3], *532 |
Index references | U51, C65, W91 |
Dual polyhedron | Small dodecahemidodecacron |
Vertex figure | ![]() 5.10.5/4.10 |
Bowers acronym | Sidhid |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Small_dodecahemidodecahedron.stl/220px-Small_dodecahemidodecahedron.stl.png)
In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U51. It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing through the model center.
Related polyhedra
[edit]It shares its edge arrangement with the icosidodecahedron (its convex hull, having the pentagonal faces in common), and with the small icosihemidodecahedron (having the decagonal faces in common).
![]() Icosidodecahedron |
![]() Small icosihemidodecahedron |
![]() Small dodecahemidodecahedron |
References
[edit]- ^ Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult.
External links
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