Small dodecahemicosahedron

Small dodecahemicosahedron
TypeUniform star polyhedron
ElementsF = 22, E = 60
V = 30 (χ = 8)
Faces by sides12{5/2}+10{6}
Wythoff symbol5/3 5/2 | 3 (double covering)
Symmetry groupIh, [5,3], *532
Index referencesU62, C78, W100
Dual polyhedronSmall dodecahemicosacron
Vertex figure
6.5/2.6.5/3
Bowers acronymSidhei

In geometry, the small dodecahemicosahedron is a nonconvex uniform polyhedron, indexed as U62. Its vertex figure is a crossed quadrilateral.

It is a hemipolyhedron with ten hexagonal faces passing through the model center.

Related polyhedra

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


Dodecadodecahedron

Small dodecahemicosahedron

Great dodecahemicosahedron

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 just colour its whole interior, the middle of the pentagrams are over empty space, as can be seen from the picture of the great dodecahemicosahedron above. Hence, some, such as Jonathan Bowers, do not fill in the middle of the pentagram: this filling has been called "neo 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]


Traditional filling

"Neo filling"

References

See also

External links

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