Platonic Solids
Tetrahedron
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
Octahedron
Face: Equilateral Triangle
Faces: 8
Edges: 12
Vertices: 6
Dihedral Angle: 109.47°
Dual: Cube
Dodecahedron
Face: Pentagon
Faces: 12
Edges: 30
Vertices: 20
Dihedral Angle: 116.57°
Dual: Icosahedron
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
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