Great disnub dirhombidodecahedron

Great disnub dirhombidodecahedron
Type	Uniform star polyhedron
Elements	F = 204, E = 240 V = 60 (χ = 32)
Faces by sides	120{3}+60{4}+24{5/2}
Wythoff symbol	| (3/2) 5/3 (3) 5/2
Symmetry group	Ih, [5,3], *532
Index references	U-, C-, W-
Bowers acronym	Gidisdrid
(5/2.4.3.3.3.4. 5/3.4.3/2.3/2.3/2.4)/2 (Vertex figure)	Great disnub dirhombidodecacron (dual polyhedron)

In geometry, the great disnub dirhombidodecahedron, also called Skilling's figure, is a uniform star polyhedron.

John Skilling discovered this one further uniform polyhedron, by relaxing the condition that only two faces may meet at an edge. Some authors do not count it as a uniform polyhedron, because some pairs of edges coincide.

It has 120 edges with 2 faces and 120 edges with 4 faces. If the 4-face edges are counted twice, as two topologically disjoint edges, this figure can be considered to have 360 total edges, and the Euler characteristic becomes -88.

The vertex figure has 4 square faces passing through the center of the model.

Related polyhedra

It shares the same edge arrangement as the great dirhombicosidodecahedron, but has a different set of triangular faces. The vertices and edges are also shared with the uniform compounds of 20 octahedra or 20 tetrahemihexahedra. 180 of the edges are shared with the great snub dodecicosidodecahedron.

Convex hull	Great snub dodecicosidodecahedron	Great dirhombicosidodecahedron
Great disnub dirhombidodecahedron	Compound of twenty octahedra	Compound of twenty tetrahemihexahedra

Dual polyhedron

The great disnub dirhombidodecacron

The dual of the great disnub dirhombidodecahedron is called a great disnub dirhombidodecacron. It is a nonconvex infinite isohedral polyhedron.

Like the visually identical great dirhombicosidodecacron in Magnus Wenninger's Dual Models, it is represented with intersecting infinite prisms passing through the model center, cut off at a certain point that is convenient for the maker. Wenninger suggested these figures are members of a new class of stellation polyhedra, called stellation to infinity. However, he also acknowledged that strictly speaking they are not polyhedra because their construction does not conform to the usual definitions.

See also

• List of uniform polyhedra

References

• Skilling, John (1975), "The complete set of uniform polyhedra", Philosophical Transactions of The Royal Society, Series A: Mathematical, Physical and Engineering Sciences 278 (1278): 111–135, doi:10.1098/rsta.1975.0022 .
• Weisstein, Eric W., "Great dirhombicosidodecahedron" from MathWorld.
• http://www.software3d.com/MillersMonster.php

External links

• http://www.orchidpalms.com/polyhedra/uniform/skilling.htm
• http://www.georgehart.com/virtual-polyhedra/great_disnub_dirhombidodecahedron.html