For questions related to polyhedra and their properties.
A polyhedron is a solid in $3$ dimensions with flat polygonal faces, straight edges and vertices. Two faces must join at each edge, and at least three must join at each vertex.
Examples consist of cubes, pyramids, stellations, etc.
Polyhedra can be defined in one of two main ways. They can be defined as a bounded intersection of half-planes, or as a connected set of polygons. The former definition restricts us to convex shapes, which are better behaved, while the latter is more relaxed, permitting star faces and face configurations.
In a convex polyhedron with $F$ faces, $E$ edges and $V$ vertices, the formula $$F-E+V=2$$ is satisfied. This is known as Euler's polyhedron formula.
Another useful result is that in a convex polyhedron, the angles of each of the faces at each vertex add up to less than $2\pi$, and the sum of all defects equals $4\pi$. This is known as Descartes' Theorem.
