From: Gerry Myerson <gerry@mpce.mq.edu.au>
Subject: Re: Number of Triangles formed by intersecring diagonals....
Date: Mon, 02 Oct 2000 11:52:59 +1000
Newsgroups: sci.math
Summary: [missing]

In article <t3YA5.23$Hv2.825@m2newsread.uni2.es>, "josevidosa" 
<josevidosa@wanadoo.es> wrote:

> ...¿Cual es la formula que da el numero de triangulos que se obtienen 
> mediante la interseccion de las diagonales en un poligono regular 
> cuando el numero de vertices es par?

You may find this useful. 

98k:52027 52B05 (51M04) 
Poonen, Bjorn(1-BELL); Rubinstein, Michael(1-BELL) 
The number of intersection points made by the diagonals of a regular 
polygon. (English. English summary) 
SIAM J. Discrete Math. 11 (1998), no. 1, 135--156 (electronic). 

Summary: "We give a formula for the number of interior intersection 
points made by the diagonals of a regular $n$-gon. The answer is a 
polynomial on each residue class modulo 2520. We also compute the 
number of regions formed by the diagonals, by using Euler's formula 
$V-E+F=2$."