2
votes
2answers
62 views

What's the fewest number of sides required to make a polytope in n dimensions?

In 2 dimensions it takes at least 3 sides to make a polygon, the triangle, and in 3 dimensions it takes at least 4 faces (so far as I'm aware) to make a polyhedron. Can this rule be generalized to ...
1
vote
0answers
68 views

Area of a 2D convex polytope made of halfspaces

For a computer program I am attempting to solve the area of a convex polytope defined by a finite number of halfspaces. I understand that this forms a polygon and given the vertices of a polygon I am ...
3
votes
1answer
192 views

Find the vertices of the polytope

Let $x,n$ be 2 integers with $x<n$. I need to find the vertices of the polytope $P$ of $2 \times n$ nonnegative matrices $A$ such that: The first row in $A$ is summed to $x$. $$\sum_{j=1}^n ...