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.

Great dodecahemidodecahedron
TypeUniform star polyhedron
ElementsF = 18, E = 60
V = 30 (χ = −12)
Faces by sides12{5/2}+6{10/3}
Wythoff symbol5/3 5/2 | 5/3 (double covering)
Symmetry groupIh, [5,3], *532
Index referencesU70, C86, W107
Dual polyhedronGreat dodecahemidodecacron
Vertex figure
5/2.10/3.5/3.10/3
Bowers acronymGidhid
3D model of a great dodecahemidodecahedron

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.

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the pentagrammic faces in common) and the great icosihemidodecahedron (having the decagrammic faces in common).


Great icosidodecahedron
Great dodecahemidodecahedron
Great icosihemidodecahedron

Icosidodecahedron (convex hull)



Traditional filling
Modulo-2 filling

See also

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