Grand ditetrahedronary hexacosidishecatonicosachoron

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Grand ditetrahedronary hexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGadtaxady
Coxeter diagramx3o3o3o5/2*a ()
Elements
Cells600 tetrahedra, 120 great stellated dodecahedra, 120 great icosidodecahedra
Faces2400 triangles, 1440 pentagrams
Edges3600
Vertices600
Vertex figureRhombitetratetrahedron, edge lengths 1 and (5–1)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGid–3–tet:
 Gissid–5/2–gid: 144°
Central density34
Number of external pieces8520
Level of complexity26
Related polytopes
ArmyHi, edge length
RegimentGadtaxady
CompanyGadtaxady
ConjugateSmall retroditetrahedronary hexacosidishecatonicosachoron
Abstract & topological properties
Flag count57600
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The grand ditetrahedronary hexacosidishecatonicosachoron, or gadtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 great icosidodecahedra. 4 great stellated dodecahedra, 4 tetrahedra, and 6 great icosidodecahedra join at each vertex, with a small rhombitetratetrahedron as the vertex figure.

The grand ditetrahedronary hexacosidishecatonicosachoron contains the vertices of a great dodecicosidodecahedral prism and decagrammic duoprism.

Cross-sections[edit | edit source]

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


Vertex coordinates[edit | edit source]

The vertices of a grand ditetrahedronary hexacosidishecatonicosachoron 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 grand ditetrahedronary hexacosidishecatonicosachoron is the colonel of a regiment with 37 members, plus 5 fissaries and three compounds (two are subsymmetric), as well as 11 scaliform members plus 54 scaliform fissaries and 2 scaliform compounds.

External links[edit | edit source]