# Chasmic cuboctachoron

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Chasmic cuboctachoron
Rank4
TypeScaliform
SpaceSpherical
Notation
Bowers style acronymCaco
Elements
Cells16 cubes, 8 blends of 2 octagonal prisms
Faces32+64 squares, 16 octagons
Edges32+128
Vertices64
Vertex figureButterfly pyramid, edge lengths 2, 2+2, 2, 2+2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{3+\sqrt2}{2}} ≈ 1.48563}$
Related polytopes
ArmySidpith
RegimentSidpith subregiment
ConjugateGreat cuboctachoron
Topological properties
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

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).