I'm reading the following description of the contraction of oriented matroid, and its connection to polytopes:
I have yet to find a numerical example to verify 6.13., but first I just want to check if my understanding is correct.
If I was to compute V/v as described, is it correct that the resulting matrix will be the coordinates of the vertices of P (except x) being "projected" into a 2-dim line (i.e. the vertex figure P/x) in the 3-dim space?
Also, in this example, P is a 2-dim polytope, and V is its vector configuration in R^3. My understanding is that V describes P after being "lifted up" one dimension. So if I was to remove that extra dimension from V/v (i.e. by deleting the corresponding row), would I recover the original vertex figure in 2-d?