Grand ditetrahedronary cubiprismatodishecatonicosachoron

Grand ditetrahedronary cubiprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gadtacapady
Elements
Cells	120 great stellated dodecahedra, 120 compounds of five cubes, 1200 triangular prisms, 120 great dodecicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagrams, 720 decagrams
Edges	3600
Vertices	600
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403$
Number of external pieces	55800
Level of complexity	147
Related polytopes
Army	Hi
Regiment	Gadtaxady
Conjugate	Small ditetrahedronary cubiprismatodishecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	3120
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The grand ditetrahedronary cubiprismatodishecatonicosachoron, or gadtacapady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 1200 triangular prisms, and 120 great dodecicosidodecahedra. Four great stellated dodecahedra, eight cubes (or four compounds), twelve triangular prisms, and twelve great dodecicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the grand ditetrahedronary hexacosidishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#871).