Grand ditetrahedronary hexacosihecatonicosachoron

Grand ditetrahedronary hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gadtaxhi
Coxeter diagram	o3o3o5x3/2*b ()
Elements
Cells	600 tetrahedra, 120 great ditrigonary icosidodecahedra
Faces	2400 triangles, 720 pentagons
Edges	3600
Vertices	600
Vertex figure	Quasitruncated tetrahedron, edge lengths 1 (triangle edges) and (1+√5)/2 (other edges)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$
Hypervolume	$5\frac{100-37\sqrt5}{4} ≈ 21.58186$
Dichoral angles	Gidtid–3–tet: $\arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876^\circ$
	Gidtid–5–gidtid: 72°
Central density	218
Number of external pieces	78000
Level of complexity	261
Related polytopes
Army	Hi
Regiment	Gadtaxady
Conjugate	Small ditetrahedronary hexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The grand ditetrahedronary hexacosihecatonicosachoron, or gadtaxhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 great ditrigonary icosidodecahedra. 4 great ditrigonary icosidodecahedra and 4 tetrahedra 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" (#856).

• Klitzing, Richard. "gadtaxhi".