Faceted rectified hecatonicosachoron

Faceted rectified hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Fry
Coxeter diagram	(x3o3o3/2x5*a)/2 (/2)
Elements
Cells	600 tetrahedra 120 truncated dodecahedra
Faces	2400 triangles 720 decagons
Edges	3600
Vertices	1200
Vertex figure	Triangular retroprism, edge lengths 1 (base) and √(5+√5)/2 (sides)
Edge figure	tet 3 tid 10 tid 10 tid 3
Measures (edge length 1)
Circumradius	${\frac {3{\sqrt {3}}+{\sqrt {15}}}{2}}\approx 4.53457$
Hypervolume	$25{\frac {693+310{\sqrt {5}}}{4}}\approx 8663.63171$
Dichoral angles	Tid–10–tid: 72°
	Tet–3–tid: $\arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.37737^{\circ }$
Central density	7
Number of external pieces	13800
Level of complexity	23
Related polytopes
Army	Rahi
Regiment	Rahi
Conjugate	Faceted rectified great grand stellated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	57600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	4
Convex	No
Nature	Tame

The faceted rectified hecatonicosachoron, or fry, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 truncated dodecahedra. Two tetrahedra and six truncated dodecahedra join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 3: Triangular Rectates" (#49).

• Klitzing, Richard. "fry".