Dodecahedron

The dodecahedron is even more graceful than the icosahedron, but unfortunately is not rigid, being formed of pentagons, so we have to cheat.

12 pentagons on the outside, this one has inner toothpics to make it rigid. Each pentagon has 5 toothpicks inside, pointing inwards, and meeting at a raisin.

Mysteriously, these interior toothpicks point at other corners of the dodecahedron, and the interior raisins form the corners of an Icosahedron - which demonstrates the duality of the icosa and dodeca hedra.

The dodecahedron is dual to the Icosahedron.

It contains 20 outer + 12 inner raisins, 30 outer toothpicks, 60 inner toothpicks.

Reinforced dodecahedron ( inwardly stellated )

Here is the same dodecahedron viewed from above...

There is a ten sided polygon ( decagon ) with two nested pentagons, some nice five cornered stars, and other things for you to spot. The whole thing is built out of regular triangles, and is strong enough to throw about the room.

Where there are five cornered stars, as there are here, there are golden ratios, and this object has those in plenty, which is why it is so aesthetically pleasing, probably.

Here is the same style of dodecahedron, but built with little bamboo kebab skewers. ( Perhaps Pythagoras would have called them Souvlaki skewers). This one is dangling, and has rotated itself so that you can see an interesting pattern containing stars, golden ratios, and other stuff. The interior icosahedron is made out of white string the same colour as the bamboo skewers, and connects the inner vertices.

Here Zorro fights a bandit dodecahedron made out of CDs. ( well, if the CDs were pentagons it would be a dodecahedron - the yellow strings are an icosidodecahedron ).