Quasidisprismatotesseractihexadecachoron

Quasidisprismatotesseractihexadecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quidpith
Coxeter diagram	x4/3o3o3x ()
Elements
Cells	16 tetrahedra, 32 triangular prisms, 8+24 cubes
Faces	64 triangles, 48+96 squares
Edges	96+96
Vertices	64
Vertex figure	Triangular retroantipodium, edge lengths 1 (small base), and √2 (large base and sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045$
Hypervolume	${\frac {32{\sqrt {2}}-43}{6}}\approx 0.37581$
Dichoral angles	Cube–4–cube: 45°
	Cube–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Tet–3–trip: 30°
Central density	7
Number of external pieces	23632
Level of complexity	1947
Related polytopes
Army	Tat, edge length ${\sqrt {2}}-1$
Regiment	Gittith
Conjugate	Small disprismatotesseractihexadecachoron
Abstract & topological properties
Flag count	3072
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The quasidisprismatotesseractihexadecachoron, or quidpith, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 32 triangular prisms, and 8+24 cubes. 1 tetrahedron, 3 triangular prisms, and 1+3 cubes join at each vertex. It is the result of pushing the cells of either a tesseract or a hexadecachoron inwards.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great tesseractitesseractihexadecachoron.

Related polychora

The quasidisprismatotesseractihexadecachoron can be blended with the octagrammic diorthoprism to form the great quasiprismatodishexadecachoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#485).

• Klitzing, Richard. "quidpith".