Great complex icosidodecahedral alterprism

The great complex icosidodecahedral alterprism is an exotic-combo-celled uniform polychoron that consists of 2 great icosahedra, 2 small stellated dodecahedra, 12 pentagrammic antiprisms, and 20 octahedra. The great icosahedra and small stellated dodecahedra lie in the same hyperplanes, forming great complex icosidodecahedron combo-cells. The octahedra go through the centre of the polychoron.

Great complex icosidodecahedral alterprism
Hossdap-reg.png
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramxo3/2xx3/2ox5/2*a&#x
Elements
Cells2 great icosahedra
2 small stellated dodecahedra
12 pentagrammic antiprisms
20 octahedra
Faces40+120 triangles
24 pentagrams
Edges60 4-fold
60 6-fold
Vertices24
Vertex figureExotic faceting of a non-uniform pentagonal antiprism
Measures (edge length 1)
Circumradius2/2 ≈ 0.70711
Height25-2/2 ≈ 0.78615
Related polytopes
ArmySemi-uniform Ipe
RegimentHossdap
Abstract & topological properties
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureExotic

Vertex coordinatesEdit

The vertices of a great complex icosidodecahedral alterprism of edge length 1 are given by all even permutations of the first three coordinates of:

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