Tesseractihexadecatruncated prismatotesseractihexadecachoron

Tesseractihexadecatruncated prismatotesseractihexadecachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Thatpath
Coxeter diagram	x3x3x4/3x4*b ()
Elements
Cells	24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, 8 cuboctatruncated cuboctahedra
Faces	96+96 squares, 64+64 hexagons, 48 octagons, 48 octagrams
Edges	192+192+192+192
Vertices	384
Vertex figure	Irregular tetrahedron, edge lengths √2 (2), √3 (2), √2+√2 (1), and √2–√2 (1)
Measures (edge length 1)
Circumradius	$\sqrt{4+\sqrt2} ≈ 2.32685$
Hypervolume	$6\left(7+12\sqrt2\right) ≈ 143.82338$
Dichoral angles	Cotco–8/3–stop: 135°
	Toe–4–stop: 135°
	Cotco–6–toe: 120°
	Cotco–8–girco: 90°
	Girco–4–stop: 90°
	Toe–6–girco: 60°
Number of external pieces	176
Level of complexity	60
Related polytopes
Army	Semi-uniform Gidpith
Regiment	Thatpath
Conjugate	Tesseractihexadecaquasitruncated prismatotesseractihexadecachoron
Convex core	Tesseract
Abstract & topological properties
Euler characteristic	–24
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The tesseractihexadecatruncated prismatotesseractihexadecachoron, or thatpath, is a nonconvex uniform polychoron that consists of 24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, and 8 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

The tesseractihexadecatruncated prismatotesseractihexadecachoron can be vertex-inscribed into a disicositetratruncated disicositetrachoron.

Cross-sections

Vertex coordinates

Vertex coordinates for a tesseractihexadecatruncated prismatotesseractihexadecachoron of edge length 1 are given by all permutations of:

• $\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 9: Omnitruncates" (#340).

• Klitzing, Richard. "thatpath".