Rectified grand hexacosichoron

Rectified grand hexacosichoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Raggix
Coxeter diagram	o5/2o3x3o ()
Elements
Cells	600 octahedra, 120 great icosahedra
Faces	1200+2400 triangles
Edges	3600
Vertices	720
Vertex figure	Pentagrammic prism, edge length 1
Measures (edge length 1)
Circumradius	$\sqrt{5-2\sqrt5} ≈ 0.72654$
Hypervolume	$25\frac{15\sqrt5-31}{4} ≈ 15.88137$
Dichoral angles	Gike–3–oct: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124°$
	Oct–3–oct: $\arccos\left(\frac{3\sqrt5-1}{8}\right) ≈ 44.47751°$
Central density	191
Number of external pieces	73440
Level of complexity	272
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Rectified hexacosichoron
Convex core	Hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The rectified grand hexacosichoron, or raggix, is a nonconvex uniform polychoron that consists of 600 regular octahedra and 120 great icosahedra. Two great icosahedra and 5 octahedra join at each pentagrammic prismatic vertex. As the name suggests, it can be obtained by rectifying the grand hexacosichoron.

Blending 10 rectified grand hexacosichora results in the great disnub dishexacosichoron, which is uniform.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified great faceted hexacosichoron.

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#119).

• Klitzing, Richard. "raggix".