There are five Platonic solids in three-dimensional space that are regular: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The dodecahedron in particular contains pentagonal faces, while the icosahedron, its dual polyhedron, has a vertex figure that is a regular pentagon.
The five Platonic solids in three-dimensional space are all regular: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The dodecahedron is characterized by its pentagonal faces, while the icosahedron has a vertex figure composed of regular pentagons.