Snub hexecontatetrasnub-snub disoctachoron

Snub hexecontatetrasnub-snub disoctachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Siggissido
Elements
Cells	192 tetrahedra, 64+96 octahedra, 8 icosahedra, 8 great icosahedra
Faces	64+64+96+96+96+192+192+192+192 triangles
Edges	48+96+96+192+192+192
Vertices	96
Vertex figure	Blend of pentagrammic cuploid and retropentagonal cuploid, edge length 1
Measures (edge length 1)
Circumradius	1
Hypervolume	Undefined
Related polytopes
Army	Sadi
Regiment	Disdi
Conjugate	Snub hexecontatetrasnub-snub disoctachoron
Convex core	Tesseract
Abstract & topological properties
Euler characteristic	–224
Orientable	No
Properties
Symmetry	B4/2, order 192
Convex	No
Nature	Tame

The snub hexecontatetrasnub-snub disoctachoron, or siggissido, is a nonconvex uniform polychoron that consists of 8 icosahedra, 8 great icosahedra, 64+96 regular octahedra, and 192 tetrahedra. 1 icosahedron, 1 great icosahedron, 4+6 octahedra, and 8 tetrahedra join at each vertex.

This polychoron has pyritotesseractic symmetry, with the icosahedra and great icosahedra acting as snub tetrahedra. It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron. With all of its cells geometrically regular, it can be considered a semiregular polychoron.

It was discovered on January 28, 2021, by Polytope Discord user _Geometer. Following the discovery of six uniforms the previous year its discovery led to the find of several hundred additional uniforms in the same regiment.

Gallery

Vertex coordinates

The vertices of a snub hexecontatetrasnub-snub disoctachoron of edge length 1, centered at the origin, are given by all even permutations of:

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

External links

• Bowers, Jonathan. "Category 30: Idtessids" (#1856).