Ditetrahedronary dishecatonicosachoron

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Ditetrahedronary dishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymDattady
Coxeter diagramo3o3o3x5/2*b ()
Elements
Cells120 great stellated dodecahedra, 120 small ditrigonary icosidodecahedra
Faces1200 triangles, 1440 pentagrams
Edges3600
Vertices600
Vertex figureSemi-uniform truncated tetrahedron, edge lengths (5–1)/2 (triangle edges) and 1 (other edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesSidtid–5/2–gissid: 144°
 Sidtid–3–sidtid: 120°
Central density9
Number of external pieces2520
Level of complexity11
Related polytopes
ArmyHi, edge length
RegimentDattady
ConjugateGreat ditetrahedronary dishecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic–600
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The ditetrahedronary dishecatonicosachoron, or dattady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 great stellated dodecahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The ditetrahedronary dishecatonicosachoron contains the vertices and edges of a hexagonal duoprism, rhombidodecadodecahedral prism, and decachoron.

Cross-sections[edit | edit source]

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


Vertex coordinates[edit | edit source]

The vertices of a ditetrahedronary dishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

Related polychora[edit | edit source]

The ditetrahedronary dishecatonicosachoron is the colonel of a regiment with 37 members, plus four fissaries and two compounds, as well as a number of scaliform members.

External links[edit | edit source]