Rank4
TypeScaliform
Notation
Bowers style acronymIrgfix
Elements
Cells24 gike, 24 sissid, 96 targi
Faces96+96+288 triangles, 288 pentagrams
Edges144+288
Vertices96
Vertex figureFaceting of tridiminished great icosahedron
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {5}}-1}{2}}\approx 0.61803}$
Hypervolume${\displaystyle \approx 0.249224}$
Related polytopes
RegimentRasdi
Abstract & topological properties
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexNo
NatureCoincidic

The icositetradiminished great faceted hexacosichoron, also called the icositetrareplenished great faceted hexacosichoron or irgfix, is a coincidic scaliform polychoron that consists of 24 great icosahedra, 24 small stellated dodecahedra, and 96 tridiminished great icosahedra. 3 great icosahedra, 3 small stellated dodecahedra, and 9 tridiminished great icosahedra meet at each vertex. It can be formed by diminishing the 24 vertices of an inscribed icositetrachoron from a great faceted hexacosichoron.

The great icosahedra and small stellated dodecahedra lie in the same hyperplanes, forming great complex icosidodecahedron combo-cells, making the polychoron coincidic.

Vertex coordinates

The vertices of an icositetradiminished great faceted hexacosichoron of edge length 1, centered at the origin, are the same as those of the retrosnub disicositetrachoron, given by all even permutations of:

• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,0\right).}$

Related polychora

This polychoron has the same edges as the retrosnub disicositetrachoron, and it also has all of its triangles as well as some additional pentagrams.