The polyhedron is obtained by successively cutting off each of the vertices of a truncated cuboctahedron (for more detail, No. 29 of the Magic Faces).
The snub cube is a semiregular convex polyhedron with two properties:
1. All faces are regular polygons of two types - a triangle and a square;
2. For any pair of vertices, there is a symmetry of the polyhedron (that is, a motion that translates the polyhedron into itself) that transforms one vertex to another.
Archimedean solids are semiregular polyhedra in the sense that their faces are regular polygons. Still, they are not the same, while the condition of one of the types of spatial symmetry: tetrahedral, octahedral, or icosahedral is preserved.
The polyhedron can be made in one of the other options - a flat-cube with a twist to the left (rotation counter-clockwise) and a twist to the right (rotation clockwise).
snub cube twisted to the left
snub cube twisted to the right