Retrofrustary hexacositrishecatonicosachoron

Retrofrustary hexacositrishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Raffixthi
Coxeter diagram	x3/2o5x5/3o3*a5*c
Elements
Cells	600 octahedra, 120 dodecadodecahedra, 120 small dodecicosidodecahedra, 120 small ditrigonal dodecicosidodecahedra
Faces	2400+2400 triangles, 1440 pentagons, 1440 pentagrams, 1440 decagons
Edges	7200+7200
Vertices	3600
Vertex figure	Crossed rectangular frustum, edge lengths 1 (top square), (1+√5)/2 and (√5–1)/2 (base rectangle), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {5}}\approx 2.23607$
Hypervolume	$5\left(99{\sqrt {5}}-100\right)\approx 606.85365$
Dichoral angles	Did–5–saddid: 108°
	Oct–3–saddid: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Did–5/2–sidditdid: 72°
	Saddid–10–sidditdid: 72°
	Oct–3–sidditdid: $\arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.76124^{\circ }$
Related polytopes
Army	Semi-uniform Xhi
Regiment	Affixthi
Conjugate	Antifrustary hexacositrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–2640
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The retrofrustary hexacositrishecatonicosachoron, or raffixthi, is a nonconvex uniform polychoron that consists of 600 octahedra, 120 dodecadodecahedra, 120 small dodecicosidodecahedra, and 120 small ditrigonal dodecicosidodecahedra. 1 octahedron, 1 dodecadodecahedron, 2 small dodecicosidodecahedra, and 2 small ditrigonal dodecicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the antifrustary hexacositrishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 16: Affixthi Regiment" (#666).

• Klitzing, Richard. "raffixthi".