Quasitruncated grand stellated hecatonicosachoron

Quasitruncated grand stellated hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quit gashi
Coxeter diagram	x5/3x5o5/2o ()
Elements
Cells	120 great dodecahedra, 120 quasitruncated small stellated dodecahedra
Faces	1440 pentagons, 720 decagrams
Edges	720+3600
Vertices	1440
Vertex figure	Pentagrammic pyramid, edge lengths (1+√5)/2 (base) and √(5–√5)/2 (side)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {13-5{\sqrt {5}}}{2}}}\approx 0.95385$
Hypervolume	$45{\frac {65-28{\sqrt {5}}}{2}}\approx 53.77717$
Dichoral angle	Quit sissid–5–gad: 72° Quit sissid–10/3–quit sissid: 72°
Central density	—14
Number of external pieces	51840
Level of complexity	148
Related polytopes
Army	Semi-uniform Tex
Regiment	Quit gishi
Conjugate	Truncated great hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	57600
Euler characteristic	–960
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	4
Convex	No
Nature	Tame

The quasitruncated grand stellated hecatonicosachoron, or quit gashi, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 quasitruncated small stellated dodecahedra. One great dodecahedron and five quasitruncated small stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the grand stellated hecatonicosachoron.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 2: Truncates" (#37).

• Klitzing, Richard. "quit gashi".