Disnub disicositetrachoron

Disnub disicositetrachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Disdi
Elements
Cells	24 small stellated dodecahedra, 24 great dodecahedra, 96 semicupolaically-faceted great icosahedra, 96 semicupolaically-faceted icosahedra
Faces	96+576 triangles, 288 pentagons, 288 pentagrams
Edges	96+144+576
Vertices	96
Vertex figure	Faceted tridiminished dodecahedron
Measures (edge length 1)
Circumradius	1
Hypervolume	Undefined
Related polytopes
Army	Sadi
Regiment	Disdi
Conjugate	Disnub disicositetrachoron
Abstract & topological properties
Orientable	No
Properties
Convex	No
Nature	Feral

The disnub disicositetrachoron, or disdi, is a nonconvex scaliform polychoron that consists of 24 small stellated dodecahedra, 24 great dodecahedra, 96 regular semicupolaically-faceted great icosahedra, and 96 semicupolaically-faceted icosahedra. 3 small stellated dodecahedra, 3 great dodecahedra, 9 semicupolaically-faceted great icosahedra, and 9 semicupolaically-faceted icosahedra meet at each vertex.

It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron.

It was found in January 2006 by Mason Green, along with the medial snub disicositetrachoron. ~15 years later, several hundred uniform polychora would be found in its regiment, starting with the snub hexecontatetrasnub-snub disoctachoron by Polytope Discord user _Geometer.

Vertex coordinates[edit | edit source]

The vertices of a disnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:

${\biggl (}\pm {\frac {1+{\sqrt {5}}}{4}},\pm {\frac {{\sqrt {5}}-1}{4}},\pm {\frac {1}{2}},0{\biggr )}$