# Great cuboctachoron

Great cuboctachoron
Rank4
TypeScaliform
SpaceSpherical
Notation
Bowers style acronymGaco
Elements
Cells16 cubes
8 blends of 2 octagrammic prisms
Faces32+64 squares
16 octagrams
Edges128 3-fold
32 4-fold
Vertices64
Vertex figureButterfly pyramid, edge lengths 2, 2-2, 2, 2-2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{3-\sqrt2}{2}} \approx 0.89045}$
Related polytopes
ArmyTat
RegimentGittith subregiment
ConjugateChasmic cuboctachoron
Topological properties
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

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.