In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria, and each is named after its number of faces.
- Tetrahedron – four equilateral triangle faces
- Cube (hexahedron) – six square faces
- Octahedron – eight equilateral triangle faces
- Dodecahedron – twelve pentagon faces
- Icosahedron – twenty equilateral triangle faces
Check out these cool Animated Platonic Solids courtesy of Wikipedia!
Making Platonic Solids
I’ve enjoyed making Paper Platonic Solids for years, and on our weekend trip to Three Rivers, CA, and studio visit with my cousin Mike Perez, I learned that what I’ve been up to with paper & glue, he’s been up to with steel & arc welders!
Trapeze Artist Alicia Vargas visiting Mike Perez’ pole barn Studio in Three Rivers, CA, where the first two of his “Platonic Solids in Disguise” hang from the ceiling.
Mike’s series is Polyhedronomics: derivatives of the regular Platonic solids in disguise. A series of 5 sculptures using one of the regular Platonic solids as the beginning framework of each piece.
Tetrahedron, by Mike Perez
Origami Cube by Glenn Zucman
Business Card Cube by Glenn Zucman. (if you take a solid like a tetrahedron or cube and hollow the shape out by the shape itself, recursively, you can create a fractal object. In the case of the cube, this object is called a “Menger Sponge.” If you repeat the process infinitely many times you have an object of infinite surface area and zero volume – in terms of kitchen or bathroom cleaning, the ultimate “quicker picker upper”. In the example here, I’ve only done one level of hollowing, for a “Level 1 Menger Sponge.” The business cards are printed from “Claudia Cookies,” a symmetry print I made of Claudia Schiffer’s face.
Cube (Hexahedron) by Mike Perez. From the series “Platonic Solids in Disguise”
Octahedron Tree Ornament, by Glenn Zucman. Paper octahedron of Alicia Silverstone’s eye, seen off-axis.
Octahedron Tree Ornament, by Glenn Zucman. Paper octahedron of Alicia Silverstone’s eye, seen on-axis.
Platonic Solids in Disguise by Mike Perez: initial armatures in progress for Octahedron & Dodecahedron.
Origami Dodecahedron by Glenn Zucman
Stained Glass Dodecahedron by Glenn Zucman
Icosahedron by Mike Perez. From the series Platonic Solids in Disguise.
Icosahedron by Glenn Zucman
Stelated Icosahedron by Glenn Zucman
Rohmbitruncated Cuboctahedron by Glenn Zucman. There are only 5 regular Platonic Solids. But there are many other polyhedra out there, as this rhombitruncated cuboctahedron is an example of.
It was exciting to see Mike take the beauty and simplicity of the Platonic Solids to a rich complexity in Platonic Solids in Disguise. I’m eager to see how his Octahedron and Dodecahedron develop. I hope to see the collection in a gallery show one day.
Sketch for “Platonic Solids in Disguise” by Mike Perz
Studio Tour with Mike Perez