Great dodecahemidodecahedron

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Great dodecahemidodecahedron
Great dodecahemidodecahedron.png
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 Great dodecahemidodecahedron vertfig.png
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.

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}, besides the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}.

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

Related polyhedra[edit]

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

Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Icosidodecahedron.png
Icosidodecahedron (convex hull)

Filling[edit]

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the 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]

Great dodecahemidodecahedron.png
Traditional filling
Great dodecahemidodecahedron 2.png
"Neo filling"

See also[edit]

References[edit]

External links[edit]