Archive for April, 2007

The 5 Platonic Solids

On Wednesday, I went with my friends to the Exploratorium, and Dad boutght us each a gift. I chose a “Plato’s Glo- Mobile” kit, where you create 5 polyhedrons, the Platonic Solids, out of sticks and soft, glow in the dark connectors. It was very fun! Here’s the story about it:

Hundreds of years ago, Plato produced the five Platonic Solids, which all were polyhedrons. There was Tetrahedron, which resembled a triangular pyramid. There was also Octahedron, the eight-triangular-sided polyhedron. Then, there was Icosahedron, which contained of twenty triangular sides. Hexahedron resembled a cube, and Dodecahedron consisted of twelve pentagonal sides.

He also associated them to five different “atoms”. Since Tetrahedron has the least sides, Plato gave it fire, the lightest “element” of that time. Additionally, it had the sharpest sides, so he thought it was responsible of the sharp pain. Octahedron had the second least sides, so he granted it the second heaviest atom, air. Icosahedron was the last one that had equilateral triangle sides, so he gave it water. He thought the Hexahedron was stable, and the Earth was stable too, so he gave it Earth. He thought Dodecahedron was very peculiar, so he gave it the Cosmos.



-60 sticks
-20 connectors
-4 faces
-4 vertices
-6 edges

Please note: when adding levels to the Tetrahedron as above, it has an interesting mathematical property to count the number of connectors and sticks. For example, when it is one level Tetrahedron, it has 4 connectors and 6 sticks; when it is two level, it has 10 connectors and 24 sticks. So if you keep adding the level, how many number connectors and sticks for you to construct 5 level Tetrahedron? how about 10 level one? (Answer in the comments of this post)



-50 sticks
-25 connectors
-8 faces
-6 vertices
-12 edges



-30 sticks
-12 connectors
-20 faces
-12 vertices
-30 edges



-90 sticks
-32 connectors
-12 faces (once stabilized, 60)



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