why only five regular solids?

Factual Questions
1

Why are there only five regular solids?

2

http://www.jimloy.com/geometry/hedra.htm

3

Explained here - http://www.jimloy.com/geometry/hedra.htm

4

Master beat me. google rules

5

The sum of the angles around a vertex must be less than 360 deg. This allows 3, 4, or 5 equilateral triangles, 3 squares, or 3 regular pentagons. This much is clear. Less clear is that all five actually exist, but they do. There are a number more of what are called semiregular solids that fail one of the conditions of regularity.

6

If you allow concavity, there are nine regular polyhedra.

7

What about in n dimensions. Is there a formula to determin how many regular polygons?

For 2 there would be infinite, for 1, I have NFI. For 3, there is 5 obviously. What about 6 or 7?

8

http://www.ics.uci.edu/~eppstein/junkyard/highdim.html