Semi-quasi-cube This is what I call a semi-quasi-cube (center-plane down) It is also a semi-stella octangula (eight-pointed star) and a semi-cuboctahedron (vector equilibrium). Both the stella octangula, and the cuboctahedron have some of the properties of a cube.
Thus, the term semi-quasi-cube.
Semi-quasi-cube This is the semi-quasi-cube inverted (center-plane up)
Cuboctahedron Two semi-quasi-cubes with their center-planes in, also called a cuboctahedron and a vector equilibrium because all the vectors (pointing out from center) have the same orientation, and the same length, which equals the length of the edges of the cuboctahedron.
At each corner of the cuboctahedron two regular triangles meet two squares in the order: 3-4-3-4
Stella Octangula Two semi-quasi-cubes with their center-planes out, also called a duotet, or stella octangula (eight-pointed star).