Snub hexecontatetrasnub-snub disoctachoron

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Snub hexecontatetrasnub-snub disoctachoron
Rank4
TypeUniform
Notation
Bowers style acronymSiggissido
Elements
Cells192 tetrahedra, 64+96 octahedra, 8 icosahedra, 8 great icosahedra
Faces64+64+96+96+96+192+192+192+192 triangles
Edges48+96+96+192+192+192
Vertices96
Vertex figureBlend of pentagrammic cuploid and retropentagonal cuploid, edge length 1
Measures (edge length 1)
Circumradius1
HypervolumeUndefined
Related polytopes
ArmySadi
RegimentDisdi
ConjugateSnub hexecontatetrasnub-snub disoctachoron
Convex coreTesseract
Abstract & topological properties
Euler characteristic–224
OrientableNo
Properties
SymmetryB4/2, order 192
ConvexNo
NatureTame

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[edit | edit source]

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]