Chasmic cuboctachoron

Chasmic cuboctachoron
Rank	4
Type	Scaliform
Notation
Bowers style acronym	Caco
Elements
Cells	16 cubes, 8 blends of 2 octagonal prisms
Faces	32+64 squares, 16 octagons
Edges	32+128
Vertices	64
Vertex figure	Butterfly pyramid, edge lengths √2, √2+√2, √2, √2+√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563$
Central density	0
Related polytopes
Army	Sidpith
Regiment	Sidpith subregiment
Conjugate	Great cuboctachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	No
Nature	Tame

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

It can be formed as a blend of a small spinoprismatotesseractioctachoron and an octagonal diorthoprism (a compound of 2 square-octagonal duoprisms). It is also a blend of four such duoprisms, with pairs of octagonal prism cells themselves blending.

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

This polychoron is in a subregiment of the small disprismatotesseractihexadecachoron, as it has its vertices but not all of its edges (specifically, it is missing one class of 32 edges).

External links

• Bowers, Jonathan. "Category S2: Podary Scaliforms" (#S14).