The dual of a regular polyhedron is also regular. The following polyhedra are combinatorially equivalent to the regular polyhedron. Applying the Petrie dual to a regular polyhedron produces a regular map. The compound of five octahedra is one of the five regular polyhedron compounds. This concept of a regular polyhedron would remain unchallenged for almost 2000 years. The most common way presented to construct a regular polyhedron is via a fold-out net. For polyhedra, a cantellation offers a direct sequence from a regular polyhedron to its dual. It is the only self-dual regular polyhedron. The cube is a regular polyhedron, and a square prism. The octahedron is a regular polyhedron, and a triangular antiprism. If faces are all irregular, it is a regular polyhedron. It depicts a nonconvex regular polyhedron known as the small stellated dodecahedron. A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is a uniform polyhedron which has just one kind of face. A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron.