Icositetradiminished faceted hexacosichoron

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Icositetradiminished faceted hexacosichoron
Rank4
TypeScaliform
Notation
Bowers style acronymIdfix
Elements
Cells24 ike, 24 gad, 96 teddi
Faces96+96+288 triangles, 288 pentagons
Edges144+288
Vertices96
Vertex figureFaceting of tridiminished icosahedron
Measures (edge length 1)
Circumradius
Hypervolume
Related polytopes
ArmySadi
RegimentSadi
ConjugateIcositetradiminished great faceted hexacosichoron
Abstract & topological properties
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexNo
NatureCoincidic

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

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

Vertex coordinates[edit | edit source]

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

Related polychora[edit | edit source]

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