Grand ditetrahedronary hexacosihecatonicosachoric antiprism

Grand ditetrahedronary hexacosihecatonicosachoric antiprism
File:Grand ditetrahedronary hexacosihecatonicosachoric antiprism.png (OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gadtaxhiap
Coxeter diagram	β2β5/2o3o3o ()
Elements
Tera	1200 pentachora, 120 great ditrigonary icosidodecahedral antiprisms, 2 grand ditetrahedronary hexacosihecatonicosachora
Cells	1200+4800 tetrahedra, 240 great ditrigonary icosidodecahedra, 720 pentagrammic antiprisms
Faces	4800+7200 triangles, 1440 pentagons
Edges	2400+7200
Vertices	1200
Vertex figure	Tetrahedron atop quasitruncated tetrahedron, edge lengths (1+√5)/2 (6 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.951057$
Height	${\sqrt {\frac {{9}{\sqrt {5}}-19}{2}}}\approx 0.749871$
Related polytopes
Army	Semi-uniform Hipe
Regiment	Gadtaxhiap
Abstract & topological properties
Flag count	518400
Orientable	Yes
Properties
Symmetry	H4×A1, order 28800
Convex	No
Nature	Tame

The grand ditetrahedronary hexacosihecatonicosachoric antiprism or gadtaxhiap, is a nonconvex uniform polyteron that consists of 2 grand ditetrahedronary hexacosihecatonicosachora, 120 great ditrigonary icosidodecahedral antiprisms, and 1200 pentachora. Each vertex joins 1 grand ditetrahedronary hexacosihecatonicosachoron, 4 great ditrigonary icosidodecahedral antiprisms, and 5 pentachora.

Despite the name and the relations that its bases have, it is not the conjugate of the small ditetrahedronary hexacosihecatonicosachoric antiprism. Its great ditrigonary icosidodecahedral antiprism facets pass through its center, making it a hemipolyteron; this does not occur in the small ditetrahedronary hexacosihecatonicosachoric antiprism.

External links

• Bowers, Jonathan. "Category 19: Miscellaneous" (#1289).

• Klitzing, Richard. "gadtaxhiap".