Retrosphenoverted trispentachoron

Retrosphenoverted trispentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Rawvtip
Coxeter diagram	o3x3x3/2o3*b ()
Elements
Cells	5 octahedra, 5 truncated tetrahedra, 5 octahemioctahedra
Faces	10+20+20 triangles, 20 hexagons
Edges	30+60
Vertices	30
Vertex figure	Crossed wedge, edge lengths 1 (base square and top edge) and √3 (side edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {35}}{5}}\approx 1.18632$
Hypervolume	${\frac {47{\sqrt {5}}}{96}}\approx 1.09474$
Dichoral angles	Oho–3-oct: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
	Oho–6–tut: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Oct–3–tut: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Oho–3–oho: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
Related polytopes
Army	Srip
Regiment	Srip
Conjugate	None
Convex core	Pentachoron
Abstract & topological properties
Flag count	1080
Euler characteristic	–5
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

The retrosphenoverted trispentachoron, or rawvtip, is a nonconvex uniform polychoron that consists of 5 regular octahedra, 5 truncated tetrahedra, and 5 octahemioctahedra. 1 octahedron, 2 truncated tetrahedra, and 2 octahemioctahedra join at each vertex.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombated pentachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#134).

• Klitzing, Richard. "rawvtip".