Great rhombic disoctachoron

Great rhombic disoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Girdo
Elements
Cells	32 triangular prisms, 8 quasitruncated hexahedra, 8 great rhombihexahedra
Faces	64 triangles, 96 squares, 48 octagrams
Edges	96+192
Vertices	96
Vertex figure	Butterfly wedge, edge lengths 1 (bases), √2–√2 (sides of outer triangles), and √2 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\sqrt {2-{\sqrt {2}}}}\approx 0.76537$
Dichoral angles	Groh–8/3–quith: 90°
	Quith–3–trip: 90°
	Groh–4–trip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Srit, edge length ${\sqrt {2}}-1$
Regiment	Wavitoth
Conjugate	Small rhombic disoctachoron
Convex core	Joined tesseract
Abstract & topological properties
Flag count	3840
Euler characteristic	–32
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The great rhombic disoctachoron, or girdo, is a nonconvex uniform polychoron that consists of 8 quasitruncated hexahedra, 8 great rhombihexahedra, and 32 triangular prisms. 2 of each type of cell join at each vertex.

It can be constructed as a blend of four quasitruncated hexahedral prisms. In the process the octagrammic prisms blend into great rhombihexahedra]]

Gallery

Vertex coordinates

The vertices are the same as those of the regiment colonel, the sphenoverted tesseractitesseractihexadecachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#223).