Pentagonal in the context of List of self-intersecting polygons

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron (a polyhedron with 12 faces) composed of regular pentagonal faces, three meeting at each vertex. It is one of the Platonic solids, described in Plato's dialogues as the shape of the universe itself. Johannes Kepler used the dodecahedron in his 1596 model of the Solar System. However, the dodecahedron and other Platonic solids had already been described by other philosophers since antiquity.

The regular dodecahedron is a truncated trapezohedron because it is the result of truncating axial vertices of a pentagonal trapezohedron. It is also a Goldberg polyhedron because it is the initial polyhedron to construct new polyhedra by the process of chamfering. It has a relation with other Platonic solids, one of them is the regular icosahedron as its dual polyhedron. Other new polyhedra can be constructed by using a regular dodecahedron.

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.

Like many basic geometric terms, the word prism (from Greek πρίσμα (prisma) 'something sawed') was first used in Euclid's Elements. Euclid defined the term in Book XI as "a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms". However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers).