Cartesian Coordinates
The Cartesian coordinates for the vertices of a cuboctahedron (of edge length √2) centered at the origin are:
- (±1,±1,0)
- (±1,0,±1)
- (0,±1,±1)
An alternate set of coordinates can be made in 4-space, as 12 permutations of:
- (0,1,1,2)
This construction exists as one of 16 orthant facets of the cantellated 16-cell.
Read more about this topic: Cuboctahedron