Mercyhurst UniversityDept of Math and ITDr Williams Home

Platonic Solids


Face: Equilateral Triangle
Faces: 4
Edges: 6
Vertices: 4
Dihedral Angle: 70.53°
Dual: Self

Hexahedron (Cube)

Face: Square
Faces: 6
Edges: 12
Vertices: 8
Dihedral Angle: 90°
Dual: Octahedron


Face: Equilateral Triangle
Faces: 8
Edges: 12
Vertices: 6
Dihedral Angle: 109.47°
Dual: Cube


Face: Pentagon
Faces: 12
Edges: 30
Vertices: 20
Dihedral Angle: 116.57°
Dual: Icosahedron


Face: Equilateral Triangle
Faces: 20
Edges: 30
Vertices: 12
Dihedral Angle: 138.19°
Dual: Dodecahedron

About the Platonic Solids

A Platonic solid is a three dimensional figure whose faces are identical regular, convex polygons. Only five such figures are possible: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. These polyhedra are named for Plato, who associated the figures with the classical elements.

Using the Applet

Drag the vertices of the planar graphs, and double click on the graph to return to its original configuration. Click and drag to turn the polyhedra, and double click to toggle auto rotation.

About this Applet

This applet was created using JavaScript and the Raphael and Three libraries. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.