Great quasiprismatodishexadecachoron

Great quasiprismatodishexadecachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gaquipadah
Elements
Cells	16 tetrahedra, 32 triangular prisms, 16 cubes, 8 octagrammic prisms
Faces	64 triangles, 32+32+64 squares, 8 octagrams
Edges	32+32+64+64
Vertices	64
Vertex figure	Blend of triangluar retroantipodium and digonal disphenoid
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$
Hypervolume	$\frac{19-8\sqrt{2}}{6} ≈ 1.28105$
Dichoral angles	Cube–4–stop: 90°
	Stop–8/3–stop: 90°
	Trip–4–stop: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$
	Cube–4–trip: $\arccos\left(\frac{\sqrt6}{3}\right) ≈ 45.26439°$
	Tet–3–trip: 30°
Related polytopes
Army	Tat
Regiment	Gittith
Conjugate	Inverted quasiprismatodishexadecachoron
Convex core	Hexadecachoron
Abstract & topological properties
Euler characteristic	8
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	No
Nature	Wild

The great quasiprismatodishexadecachoron, or gaquipadah, is a nonconvex uniform polychoron consisting of 16 regular tetrahedra, 24 triangular prisms, 16 cubes, and 8 octagrammic prisms. 1 tetrahedron, 3 triangular prisms, 2 cubes, and 2 octagrammic prisms meet each vertex. It can be created by blending a quasidisprismatotesseractihexadecachoron with an octagrammic diorthoprism, the inscribed compound of 2 square-octagrammic duoprisms. In the process 16 cubical cells blend out.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 20: Miscellaneous" (#984).

• Klitzing, Richard. "gaquipadah".