Regular polyhedron A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all …

The 5 Platonic Solids are all regular polyhedra. A regular polyhedron has: Faces that are identical regular polygons. the same number of faces meet at each vertex (corner).

Regular polyhedra generalize the notion of regular polygons to three dimensions. They are three-dimensional geometric solids which are defined and classified by their faces, vertices, and edges.

Dec 22, 2025 · Using this definition, there are a total of nine regular polyhedra, five being the convex Platonic solids and four being the concave (stellated) Kepler-Poinsot polyhedra. However, the term …

Nov 9, 2022 · It forms part of Book XIII, Proposition 18 of Euclid’s magnum opus, The Elements (written c. 300 BC). So let’s now consider how each regular polygon can be used to make regular polyhedra. …

Regular polyhedra have identical faces and equal angles. Their faces are regular polygons, all congruent. The angles and dihedral angles are also congruent. Regular polyhedra are also known as …

Regular polyhedra are polyhedra in which all the faces are congruent (identical in form) regular polygons, and the same number of faces meet at each vertex. The regular polyhedrons are the …

Only the Platonic solids are regular polyhedra; prisms and pyramids are irregular polyhedra. A Platonic solid, also referred to as a regular polyhedron, is a polyhedron whose faces are all congruent regular …

A regular polyhedron is a three-dimensional, closed shape where all the faces are identical regular polygons. The length of all sides and all angles are, therefore, equal. There are only nine regular …

Regular polyhedra generalize the notion of a regular polygon to three dimensions. A regular polyhedron is a polyhedron with congruent faces and identical vertices. There are only five convex regular …