Small pentagrammal antiprismatoverted dishecatonicosachoron

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Small pentagrammal antiprismatoverted dishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSpapivady
Coxeter diagram(x5o5/2o5x5/3*a)/2 (/2)
Elements
Cells
Faces
Edges3600
Vertices720
Vertex figurePentagrammic antiprism, edge lengths (1+5)/2 (base) and (5–5)/2 (side)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angleQuit sissid–10/3–quit sissid: 144°
Gad–5–quit sissid: 108°
Central density54
Number of external pieces32640
Level of complexity76
Related polytopes
ArmyRox
RegimentRagishi
ConjugateGreat pentagonal retroprismatoverted dishecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count57600
Euler characteristic–960
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits4
ConvexNo
NatureTame

The small pentagrammal antiprismatoverted dishecatonicosachoron, or spapivady, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 quasitruncated small stellated dodecahedra. 2 great dodecahedra and 10 quasitruncated small stellated dodecahedra join at each vertex.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.

Vertex coordinates[edit | edit source]

The vertices are the same as those of its regiment colonel, the rectified great stellated hecatonicosachoron.

External links[edit | edit source]