# Great dodecahemidodecahedron

Great dodecahemidodecahedron
Type Uniform star polyhedron
Elements F = 18, E = 60
V = 30 (χ = −12)
Faces by sides 12{5/2}+6{10/3}
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

In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. 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.

## Related polyhedra

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)

## Filling

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, "neo filling" is sometimes used instead as a more accurate filling. In neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in).[1]