As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Wednesday, April 21, 2010

### V+F-E=2

Euler's celebrated polyhedron formula V+F-E=2 is part of the MT365 course. Worked on question 3 of MT365 TMA01 today ( close to the cut-off date by the way ). It was a proof which required V+F-E=2 and two Handshaking Lemma's: one for graphs and for one polyhedra.

A few years ago I read that Euler proved that the only possible -regular- polyhedra are:
- the Tetrahedron with triangle faces and V4-F4-E6,
- the Cube with square faces and V8-F6-E12,
- the Icosahedron with triangle faces and V6-F8-E12,
- the Dodecahedron with pentagon faces and V20-F12-E30 and finally,
-  the Icosahedraon with triangle faces and V12-F20-E30.

I think that I can prove this now too, if I can start from V+F-E=2 that is. I can at least reproduce the regular polyhedra. Part of question 3 was giving the names of at least three semi regular polyhedra with both triangle faces and pentagon faces.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)