Great complex icosidodecahedral alterprism

Great complex icosidodecahedral alterprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	xo3/2xx3/2ox5/2*a&#x
Elements
Cells	2 great icosahedra 2 small stellated dodecahedra 12 pentagrammic antiprisms 20 octahedra
Faces	40+120 triangles 24 pentagrams
Edges	60 4-fold 60 6-fold
Vertices	24
Vertex figure	Exotic faceting of a non-uniform pentagonal antiprism
Measures (edge length 1)
Circumradius	√2/2 ≈ 0.70711
Height	√2√5-2/2 ≈ 0.78615
Related polytopes
Army	Semi-uniform Ipe
Regiment	Hossdap
Abstract & topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Exotic

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.

Vertex coordinates

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

• ${\Biggl (}0,\pm {\frac {1}{2}},\pm {\frac {{\sqrt {5}}-1}{4}},\pm {\frac {\sqrt {2{\sqrt {5}}-2}}{4}}{\Biggr )}$