She cut empty cereal boxes to make regular polygons: 6 squares, 12 regular pentagons, and 32 equilateral triangles. Using small pieces of masking tape, she carefully formed the five Platonic solids. Then she mixed flour and water into a runny paste. She tore an old newspaper into small strips and soaked them in the paste. She covered each solid with a thin layer of paper.
Alex let the final layer of papier-mâché dry for two days. Then she painted the solids with a white primer, followed by bright colors. She chose colors to reflect the Greek elements traditionally associated with each shape:
- red for the tetrahedron (fire)
- green for the cube (earth)
- yellow for the octahedron (air)
- blue for the icosahedron (water)
- purple for the dodecahedron (which was the symbol for the cosmos)
One last step: When the paint was dry, Alex glued string to each solid and tied them to sticks. The gift was finished — a mathematical mobile to hang over her baby sister’s crib.
History: The Platonic Solids
The philosopher Plato insisted that his students study mathematics, especially the ideas of the Pythagoreans. Even though the five regular polyhedra (Greek for “many faces”) had been known for at least 100 years before Plato founded his Academy, mathematicians call them the Platonic solids in his honor.
Each Platonic solid is made of regular polygons (Greek for “many sides”) — polygons with all sides and angles equal, like squares — connected to make a 3-dimensional figure such that every side and corner (called a vertex) is the same from every direction. Many people are surprised to discover that there can only be five Platonic solids. Here they are:
- Tetrahedron: Four triangular faces, like a triangular pyramid.
- Cube: Six square faces, the most common Platonic solid.
- Octahedron: Eight triangular faces, like two Egyptian pyramids glued together at their bases.
- Dodecahedron: Twelve pentagonal faces, like a poorly-formed soccer ball.
- Icosahedron: Twenty triangular faces, with five triangles coming together at each corner.
Puzzle for You
- Why is an Egyptian pyramid not a Platonic solid?
To Be Continued…
Read all the posts from the November/December 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.