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${\displaystyle {\frac {1+{\sqrt {5}}}{2}}\approx 1.61803}$
Hypervolume${\displaystyle \approx 80.2492}$
Related polytopes
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

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:

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

## Related polychora

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