Inverted quasiprismatodishexadecachoron

Inverted quasiprismatodishexadecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Iquipadah
Elements
Cells	16 tetrahedra, 32 triangular prisms, 16 cubes, 8 octagonal prisms
Faces	64 triangles, 32+32+64 squares, 8 octagons
Edges	32+32+64+64
Vertices	64
Vertex figure	Blend of triangular antipodium and digonal disphenoid
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563$
Hypervolume	${\frac {19+8{\sqrt {2}}}{6}}\approx 5.05228$
Dichoral angles	Tet–3–trip: 150°
	Cube–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Cube–4–op: 90°
	Op–8–op: 90°
	Trip–4–op: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Central density	1
Number of external pieces	80
Level of complexity	30
Related polytopes
Army	Sidpith
Regiment	Sidpith
Conjugate	Great quasiprismatodishexadecachoron
Convex core	Tesseract
Abstract & topological properties
Flag count	3072
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	No
Nature	Wild

The inverted quasiprismatodishexadecachoron, or iquipadah, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 32 triangular prisms, 16 cubes, and 8 octagonal prisms. 1 tetrahedron, 3 triangular prisms, 2 cubes, and 2 octagonal prisms meet at each vertex.

It can be created by blending a small disprismatotesseractihexadecachoron with an octagonal diorthoprism, an inscribed compound of 2 square-octagonal duoprisms. In the process 16 cubical cells blend out.

Its vertex figure is concave, a property shared by sanbathi.

Jonathan Bowers wrote that the acronym iquipadah occurred to him in church before actually discovering the figure.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 20: Miscellaneous" (#983).

• Klitzing, Richard. "iquipadah".