Great cuboctachoron

Great cuboctachoron
Rank	4
Type	Scaliform
Space	Spherical
Notation
Bowers style acronym	Gaco
Elements
Cells	16 cubes 8 blends of 2 octagrammic prisms
Faces	32+64 squares 16 octagrams
Edges	128 3-fold 32 4-fold
Vertices	64
Vertex figure	Butterfly pyramid, edge lengths √2, √2-√2, √2, √2-√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} \approx 0.89045$
Related polytopes
Army	Tat
Regiment	Gittith subregiment
Conjugate	Chasmic cuboctachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	No
Nature	Tame

The great cuboctachoron or gaco is a scaliform polychoron that consists of 16 cubes and 8 blends of 2 octagrammic prisms. Two cubes and three blends of 2 octagrammic prisms meet at each vertex.

It can be formed as a blend of a great spinoprismatotesseractioctachoron and an octagrammic diorthoprism.

It has the same vertex figure as the great rhombihexahedral prism; the equilateral triangles still correspond to cubes, but the butterfly corresponds instead to a great rhombihexahedron and the isosceles triangles to octagrammic prisms.

This polychoron is in a subregiment of gittith, as it has its vertices and some but not all of its edges.

External links

• Bowers, Jonathan. "Category S2: Podary Scaliforms" (#S20).