03 Platonic solids: In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

This is the one die which is not a Platonic Solid.

This is based upon a specific platonic solid known as the octahedron.

This is based upon a specific platonic solid known as the octahedron.

The faces of each Platonic Solid are all identical regular polygons.

Each face of each Platonic solid is a convex regular polygon.

Each face of a Platonic Solid is the same regular sized polygon.

Illustration of a Cuboctahedron by Leonardo da Vinci for Luca Pacioli’s De Divina Proportione (1509)

Icosahedron -The fifth Platonic Solid is a triangle with twenty (20) faces and represents the element of water.

Hexahedron - The second Platonic Solid is a square with six (6) faces and represents the element earth.

The method can be applied to image data representing outward views from the vertices or centroids of faces of any Platonic solid.

The fifth Platonic Solid, the dodecahedron, Plato obscurely remarks, "...the god used for arranging the constellations on the whole heaven" (Timaeus 55).

The fifth Platonic Solid, the dodecahedron, Plato obscurely remarks, ...the god used for arranging the constellations on the whole heaven (Timaeus 55).

And the pictures are direct and abstract enough to be in a sense timeless (much like a Platonic solid from ancient Egypt looks the same as one today).

This installation is a platonic solid comprising 12 vertices and 30 edges, with 20 equilateral triangular faces that allow the dancer to compare his or her movements with the dimensions in space.