Retrosphenoverted tesseractitesseractihexadecachoron

Retrosphenoverted tesseractitesseractihexadecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Rawvatoth
Coxeter diagram	o3x3o4/3x4*b ()
Elements
Cells	16 octahedra, 8 truncated cubes, 8 small cubicuboctahedra
Faces	64+64 triangles, 24 squares, 48 octagons
Edges	96+192
Vertices	96
Vertex figure	Crossed wedge, edge lengths 1 (base square), √2 (top edge), and √2+√2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Hypervolume	${\frac {28+17{\sqrt {2}}}{3}}\approx 17.34721$
Dichoral angles	Socco–3–oct: 120°
	Socco–8–tic: 90°
	Socco–4–socco: 90°
	Oct–3–tic: 60°
Central density	3
Related polytopes
Army	Srit
Regiment	Srit
Conjugate	Sphenoverted tesseractitesseractihexadecachoron
Convex core	Tesseract
Abstract & topological properties
Flag count	3456
Euler characteristic	–24
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The retrosphenoverted tesseractitesseractihexadecachoron, or rawvatoth, is a nonconvex uniform polychoron that consists of 16 regular octahedra, 8 truncated cubes, and 8 small cubicuboctahedra. 1 octahedron, 2 truncated cubes, and 2 small cubicuboctahedra join at each vertex.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#141).

• Klitzing, Richard. "rawvatoth".