Great_dodecahemidodecahedron
Great dodecahemidodecahedron
Polyhedron with 18 faces
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.
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 |
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.