Small blendic disprismatodishecatonicosachoron
|Small blendic disprismatodishecatonicosachoron|
|Bowers style acronym||Sabbadipady|
|Cells||720 pentagonal prisms, 720 pentagrammic prisms, 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra|
|Faces||3600 squares, 1440 pentagons, 1440 pentagrams, 720 decagrams|
|Vertex figure||Augmented 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)|
|Dichoral angles||Gissid–5/2–stip: 162°|
|Quit sissid–10/3–quit sissid: 144°|
|Quit sissid–5–pip: 126°|
|Number of external pieces||18840|
|Level of complexity||65|
|Conjugate||Great blendic disprismatodishecatonicosachoron|
|Convex core||Chamfered hecatonicosachoron|
|Abstract & topological properties|
|Symmetry||H4, order 14400|
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]
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]
- Bowers, Jonathan. "Category 26: Blends" (#1462).
- Klitzing, Richard. "sabbadipady".