What is your motivation to do that?
You clearly underestimate such task, simply because the number of vertices of simplex grow very fast with the dimension.
I see your inequality constrainst are 72 (C matrix) assuming they are independent and number of variable is 34. Then the number of vertices can go as big as
Warning: Result may not be exact. Coefficient is greater than 9.007199e+15 and is only accurate to 15 digits
> In nchoosek (line 92)
If you project on subspace defined by A ane E (20+2 rows) then you get a subspace of dimension 12, then the number of vertices is still very large
To store all of them you need
Each of the vertices require to solve a linear system of 34 x 34.
There is very little chance that you could find a method to do it in reasonably time and with enough accuracy.
Generate a random points to cover such shape? Good luck!!!