Intelligence

[The Brain]

Originally posted by Six-Pack
Please, post something intelligent here. This board needs it.

<i>What's the pattern in this sequence?

infinity, five, six, three, three, three, three,...

In 2 dimensions, the most symmetrical polygons of all are the `regular polygons'. All the edges of a regular polygon are the same length, and all the angles are equal. If you only count the convex ones, it's easy to list all the regular polygons: the equilateral triangle, the square, the regular pentagon, and so on. In short, there is an INFINITY of regular polygons: one with n sides for each n > 3. (The cases n = 0,1, and 2 are bit degenerate.)
In 3 dimensions, the most symmetrical polyhedra of all are the `regular polyhedra', also known as the `Platonic solids'. All the faces of a Platonic solid are regular polygons of the same size, and all the vertices look identical. We also demands that our Platonic solids be convex. There are only FIVE Platonic solids:


The tetrahedron, with 4 triangular faces.
The cube, with 6 square faces.
The octahedron, with 8 triangular faces.
The dodecahedron, with 12 pentagonal faces.
The icosahedron, with 20 triangular faces. </i>

Shall I continue? Or has your brain already imploded?