Great rhombiprismic disoctachoron

Great rhombiprismic disoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Girpdo
Elements
Cells	32 hexagonal prisms, 8 great rhombihexahedra, 8 quasitruncated cuboctahedra
Faces	96+96 squares, 64 hexagons, 48 octagrams
Edges	96+192+192
Vertices	192
Vertex figure	Butterfly pyramid, base edge lengths √2–√2, √2, √2–√2, √2; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7-3{\sqrt {2}}}{2}}}\approx 1.17417$
Dichoral angles	Groh–8/3–quitco: 90°
	Quitco–6–hip: 90°
	Groh–4–hip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
	Quitco–4–hip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Semi-uniform Proh, edge lengths ${\sqrt {2}}-1$ (truncated cubes), $2-{\sqrt {2}}$ (bases of triangular prisms)
Regiment	Gichado
Conjugate	Small rhombiprismic disoctachoron
Abstract & topological properties
Flag count	6144
Euler characteristic	–32
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The great rhombiprismic disoctachoron, or girpdo, is a nonconvex uniform polychoron that consists of 8 great rhombihexahedra, 8 quasitruncated cuboctahedra, and 32 hexagonal prisms. One great rhombihexahedron, two quasitruncated cuboctahedra, and two hexagonal prisms join at each vertex.

It can be constructed as a blend of four quasitruncated cuboctahedral prisms. In the process, their cube cells blend out and their octagrammic prism cells blend into great rhombihexahedra.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#396).

• Klitzing, Richard. "girpdo".