Platonic Solids

“Platonic Solids” by Paul Vexler

Mahogany and Fir, 2009
Robert J. Drewel Building (2nd Floor Mezzanine)
Everett, WA

The Platonic Solids are a set of five polyhedra or faceted figures.  Although they are named after the famous Greek philosopher, they were studied and admired by many cultures in the ancient world.  

This set is also known as the five regular convex polyhedra because they all have the following features:

Name # of Faces # of Edges # of Verticies
Tetrahedron 4 6 4
Hexahedron (cube)  6 12 8
Octahedron 8 12 6
Icosahedron 20 30 12
Dodecahedron 12 30 20


  • All of the faces are regular, identical polygons.
  • All of the vertices have the same number of faces surrounding them.
  • The angles between any two adjacent faces (the dihedral angle) are equal.

These are the only shapes that have all of these characteristics.

Through the ages, the polyhedra have been studied by philosophers, mathematicians, artists, astronomers and scientists.  They have been associated with various mystical and cosmological schools of thought.  Their natural beauty is undeniable.