One of the
archimedean solids, the snub cube is defined by
vertices containing one
square and four
equilateral triangles each. The resulting solid has six square faces separated by 32 triangular faces. The square faces are parallel to the faces of a
cube, and do not touch. Eight of the triangular faces touch three different squares at their corners, and the remaining 24 touch one square at a corner and another square along an edge.
Oddly enough, given the uniform manner in which it is constructed, the snub cubes it lacks bilateral symmetry, and comes in distinct left-handed and right-handed forms. The only other archimedean solid with this property is the snub dodecahedron.