Small blendic disprismatodishecatonicosachoron

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Small blendic disprismatodishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSabbadipady
Coxeter diagramx5/3x5o3o5/2xØ*a
Elements
Cells720 pentagonal prisms, 720 pentagrammic prisms, 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra
Faces3600 squares, 1440 pentagons, 1440 pentagrams, 720 decagrams
Edges1200+3600+3600
Vertices2400
Vertex figureAugmented triangular antipodium, edge lengths (5–1)/2 (unaugmented base), (1+5)/2 (augmented base), 2 (antipodium sides), and (5–5)/2 (augment sides)
Measures (edge length 1)
Circumradius2
Hypervolume
Dichoral anglesGissid–5/2–stip: 162°
 Stip–4–pip:
 Quit sissid–10/3–quit sissid: 144°
 Quit sissid–5–pip: 126°
Central density16
Number of external pieces18840
Level of complexity65
Related polytopes
ArmySidpixhi
RegimentSabbadipady
ConjugateGreat blendic disprismatodishecatonicosachoron
Convex coreChamfered hecatonicosachoron
Abstract & topological properties
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small blendic disprismatodishecatonicosachoron, or sabbadipady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra, 720 pentagonal prisms, and 720 pentagrammic prisms. 1 great stellated dodecahedron, 3 pentagonal prisms, 3 pentagrammic prisms, and 3 quasitruncated small stellated dodecahedra join at each vertex.

It contains the vertices and edges of a truncated great grand hecatonicosachoron, quasitruncated small stellated hecatonicosachoron, and small disprismatodishecatonicosachoron, which each use all of its vertices. It can also be constructed as the blend of the latter two, with the common dodecahedral cells blending out.

Cross-sections[edit | edit source]

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


Vertex coordinates[edit | edit source]

The vertices of a small blendic disprismatodishecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:

Related polychora[edit | edit source]

The small blendic disprismatodishecatonicosachoron is the colonel of a regiment that includes 12 uniform members, along with 4 fissaries and 3 mixed compounds.

External links[edit | edit source]