Great retroinverted dodecahedronary hexacosihecatonicosachoron

Great retroinverted dodecahedronary hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gridixhi
Elements
Cells	600 tetrahedra, 120 small ditrigonary icosidodecahedra
Faces	2400 triangles, 720 pentagrams
Edges	1200
Vertices	120
Edge figure	(tet 3 sidtid 5/2 sidtid 3)×3
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {105{\sqrt {5}}}{4}}\approx 58.69678$
Dichoral angles	Tet–3–sidtid: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Sidtid–5/2–sidtid: 72°
Number of external pieces	116640
Level of complexity	286
Related polytopes
Army	Ex, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Sishi
Conjugate	Small retroinverted dodecahedronary hexacosihecatonicosachoron
Abstract & topological properties
Flag count	43200
Euler characteristic	1320
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Feral

The great retroinverted dodecahedronary hexacosihecatonicosachoron, or gridixhi, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra and 600 tetrahedra. Twenty small ditrigonary icosidodecahedra and twenty tetrahedra join at each vertex.

It also has great complex icosidodecahedra as exotic pseudofacets.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 17: Sishi Regiment" (#771).

• Klitzing, Richard. "gridixhi".