How to find vertices a the polytope-intersection of two simplices, if I know the vertices of these simplices.
More precisely:
Let $T_1$ and $T_2$ be two regular $n-1$ dimensional simplices with vertices $(t,0,\ldots,0), (0,t,\ldots, 0),\ldots, (0, 0, \ldots, t)$ and $(t-n+1,1,\ldots, 1), (1, t-n+1, \ldots, 1), \ldots, (1,1, \ldots, t-n+1)$ resp.
The intersection of these simplices is a polytope $P$.
How to find vertices of it?