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.

Wikipedia

Sketches by Mike Perez detailing construction plans for "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 – 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!

animated gif of a tetrahedronanimated gif of a cubeanimated gif of an octahedronanimated gif of a dodecahedronanimated gif of an icosahedron

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!

Photo of a workshop with a pole barn roof and various wood and metal machines. From the ceiling hang welded steel sculptures in the forms of articulated or "Disguised" Tetrahedron and Cube.
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.

an articulated, dense, aggressive "Tetrahedron in Disguise" made of welded steel elements
Tetrahedron, by Mike Perez
a cube shape made out of folded paper elements
Origami Cube by Glenn Zucman
A Level 1 Menger Sponge made of business cards
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.
A heavily articulated steel cube with many welded elements
Cube (Hexahedron) by Mike Perez. From the series “Platonic Solids in Disguise”
Paper model of the Octahedron Platonic Solid
Octahedron Tree Ornament, by Glenn Zucman. Paper octahedron of Alicia Silverstone’s eye, seen off-axis.
Paper model of the Octahedron Platonic Solid
Octahedron Tree Ornament, by Glenn Zucman. Paper octahedron of Alicia Silverstone’s eye, seen on-axis.
Welded steel armatures of the Platonic Solids "Octahedron" and "Dodecahedron"
Platonic Solids in Disguise by Mike Perez: initial armatures in progress for Octahedron & Dodecahedron.
a hollow dodecahedron made of folded paper
Origami Dodecahedron by Glenn Zucman
the Platonic Solid Dodecahedron made of blue and orange pentagons of stained glass
Stained Glass Dodecahedron by Glenn Zucman
A welded metal Icosahedron featuring many small pieces of rod, nails, and other elements articulating the core armature of an icosahedron
Icosahedron by Mike Perez. From the series Platonic Solids in Disguise.

a paper model of an icosahedron
Icosahedron by Glenn Zucman
paper model of an icosahedron with each face articulated by a tetrahedron
Stelated Icosahedron by Glenn Zucman

Paper model of the "Rhombitruncated Cuboctahedron" polyhedra, featuring 6 octahedron faces, 8 hexagon faces, and 12 square faces
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.
Paper model of a Dodecahedron-Isocshedron compound
And here’s a model of a Dodecahedron-Icosahedron compound that Mike made about 20-30 years ago!

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.

pencil on paper sketch showing plans for making steel sculptures
Sketch for “Platonic Solids in Disguise” by Mike Perz
Mike Perez giving a tour of the facilities at his studio in Three Rivers, CA
Studio Tour with Mike Perez

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