Snubification is a polyhedron operation which separates the faces of a suitable polyhedron, rotates them through a common angle, and inserts new triangular faces between the rotated faces. The angle is chosen so that the new edges have a common length. Unlike truncation, snubification has a handedness and generally produces a pair of enantiomorphic polyhedra.
Applied to the cube or octahedron, snubification gives the snub cube. Applied to the dodecahedron or icosahedron, it gives the snub dodecahedron.
