0
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1answer
16 views

Polyhedra Intersection

Suppose we are given two polyhedra defined as $P_1 = \{x | A_1x \le b_1\}$ and $P_2 = \{x | A_2x \le b_2\}$. How can we show that if $P_1$ and $P_2$ dont not intersect, then there exists vectors $s,t ...
1
vote
1answer
81 views

Bounded polyhedra closed under rotation, intersection and complement

Are there any known types of bounded polyhedra, which exist in all Euclidean dimensions, and are are closed under intersection, rotation and relative complement? In other words, I am looking for a set ...
2
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1answer
185 views

How to determine the intersection of 6 planes?

ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge. I want to prove that the 6 ...