Quasiprismatotetracontoctachoron

Quasiprismatotetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quippic
Coxeter diagram	x3o4/3o3x ()
Elements
Cells	48 octahedra, 192 triangular prisms
Faces	384 triangles, 288 squares
Edges	576
Vertices	144
Vertex figure	Square retroprism, edge lengths 1 (base) and √2 (sides)
Edge figure	oct 3 trip 4 trip 4 trip 3
Measures (edge length 1)
Circumradius	$\sqrt{2-\sqrt2} ≈ 0.76537$
Hypervolume	$2(8\sqrt2-11) ≈ 0.62742$
Dichoral angles	Oct–3–trip: 30°
	Trip–4–trip: $\arccos\left(\frac{2\sqrt2}{3}\right) ≈ 19.47122°$
Number of external pieces	154560
Level of complexity	2686
Related polytopes
Army	Spic
Regiment	Giddic
Conjugate	Small prismatotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The quasiprismatotetracontoctachoron, or quippic, is a nonconvex uniform polychoron that consists of 48 regular octahedra and 192 triangular prisms. 2 octahedra and 8 triangular prisms join at each vertex. It is the result of pushing the cells of an icositetrachoron inwards.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#533).

• Klitzing, Richard. "quippic".