Grand ditetrahedronary prismatocubihexacosihecatonicosachoron

Grand ditetrahedronary prismatocubihexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gadtap caxhi
Elements
Cells	600 tetrahedra, 120 great icosidodecahedra, 120 compounds of five cubes, 720 pentagrammic prisms
Faces	2400 triangles, 3600 squares, 1440 pentagrams
Edges	3600
Vertices	600
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403$
Number of external pieces	92400
Level of complexity	315
Related polytopes
Army	Hi
Regiment	Gadtaxady
Conjugate	Small ditetrahedronary prismatocubihexacosihecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	2400
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The grand ditetrahedronary prismatocubihexacosihecatonicosachoron, or gadtap caxhi, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 120 great icosidodecahedra, 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), and 720 pentagrammic prisms. Four tetrahedra, six great icosidodecahedra, eight cubes (or four compounds), and twelve pentagrammic prisms 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" (#863).