The Platonic Solids
In order of complexity, these are:
| Tetrahedron | 4 | equilateral triangles |
| Hexahedron / Cube | 6 | squares |
| Octahedron | 8 | equilateral triangles |
| Dodecahedron | 12 | regular pentagons |
| Icosahedron | 20 | equilateral triangles |
Those who play games like Dungeons & Dragons are probably already familiar with these.
Johannes Kepler liked to study these!
Johannes Kepler (1571-1630), best known for his three laws of planetary motion, was one of the most outstanding mathematicians of his day. In addition to his astronomical accomplishments, he systematized and extended all that was known about polyhedra in his time. While previous artist/geometers discovered particular polyhedra, he took a more mathematical approach: he defined classes of polyhedra, discovered the members of the class, and proved that his set was complete.
- from http://www.georgehart.com/virtual-polyhedra/kepler.html
Kepler also believed these polyhedra were associated with the elements:
| Tetrahedron | Fire | It has the "shape" of fire; and there's also the fire tetrahedron teaching tool, which is neat! |
| Hexahedron / Cube | Earth | It's very stable. |
| Octahedron | Air | If you hold this model lightly by the two farthest corners, and then blow, it will spin like a top! |
| Dodecahedron | the Cosmos | It has twelve faces, and there are the twelve constellations (in astrology, zodiac). |
| Icosahedron | Water | It has a similar property of that octahedron, like it moves easily or wants to move, the way fluids do. |
Origami
So I finally got around to making origami models of each! These are modular skeletons:
| Tetrahedron | 6 units | Francis Ow's 120-degree module |
| Hexahedron / Cube | 12 | Bennett Arnstein's Variation of Lewis Simon's Decoration Box modules |
| Octahedron | 6 | Lewis Simon's Gyroscope module |
| Dodecahedron | 30 | Lewis Simon's / Bob Neale's 108-degree module |
| Icosahedron | 60 | Francis Ow's 120-degree module |
...more later?
--Charlie
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