Great hexadecafaceted prismatotesseractioctachoron

Great hexadecafaceted prismatotesseractioctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gahfipto
Coxeter diagram
Elements
Cells	32 triangular prisms, 8 cubes, 8 quasirhombicuboctahedra
Faces	64 triangles, 48+96 squares
Edges	96+96
Vertices	64
Vertex figure	Triangular hemipodium, edge lengths √2 (top triangle and sides) and 1 (base pseudo-triangle)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$
Dichoral angles	Querco–4–cube: 90°
	Querco–3–trip: 90°
	Querco–4–trip: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$
Number of external pieces	2824
Level of complexity	343
Related polytopes
Army	Tat
Regiment	Gittith
Conjugate	Small hexadecafaceted prismatotesseractioctachoron
Abstract & topological properties
Euler characteristic	32
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The great hexadecafaceted prismatotesseractioctachoron, or gahfipto, is a nonconvex uniform polychoron that consists of 8 quasirhombicuboctahedra, 8 cubes, and 32 triangular prisms. Three quasirhombicuboctahedra, one cube, and three triangular prisms join at each vertex.

It also has 16 tetrahedra and 24 cubes as pseudofacets.

It can be constructed as a blend of four quasirhombicuboctahedral prisms. In the process some of the cubical cells blend out. Alternatively, it can be thought of as a blend of four great cubicuboctahedral prisms. In the process the octagrammic prism side cells blend with the base great cubicuboctahedra to produce the quasirhombicuboctahedra.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#488).

• Klitzing, Richard. "gahfipto".