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Great dodecahemidodecahedron information


Great dodecahemidodecahedron
Type Uniform star polyhedron
Elements F = 18, E = 60
V = 30 (χ = −12)
Faces by sides 12{5/2}+6{10/3}
Coxeter diagram
Wythoff symbol 5/3 5/2 | 5/3 (double covering)
Symmetry group Ih, [5,3], *532
Index references U70, C86, W107
Dual polyhedron Great dodecahemidodecacron
Vertex figure
5/2.10/3.5/3.10/3
Bowers acronym Gidhid
3D model of a great dodecahemidodecahedron

In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.

Aside from the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}, it is the only nonconvex uniform polyhedron whose faces are all non-convex regular polygons (star polygons), namely the star polygons {5/2} and {10/3}.

It is a hemipolyhedron with 6 decagrammic faces passing through the model center.

  1. ^ Maeder, Roman. "70: great dodecahemidodecahedron". MathConsult.

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