polyhedron

If there are one or more houses in that half, then we let this half be our new polyhedron.

This rectangle is a special case of a convex polyhedron.

A different unfolding of the polyhedron may yield a shorter path.

For example, if I have something like a polyhedron, I'll declare that as an array of points.

I was not aware of Conway polyhedron notation.

This subgradient cuts our polyhedron roughly in half.

It probably just means to say "holds true for every regular polyhedron".

I just love the vertex, line, polygon, polyhedron operations.

Interesting that this also works for a degenerate polyhedron with 3 vertices, 3 edges, and 2 faces.

I keep hoping someone will use Jason Davies' D3 map stuff to project a globe on a polyhedron and then split it over multiple pages so you can make larger globes, and add tabs for gluing.

[We assume that the polyhedron has positive area and otherwise handle the case in a different way by a standard unidimensional search.

If we pick a vertex on a polyhedron and start marching across a face, in order for that to be a geodesic, how do we continue when we cross an edge onto an adjacent face?

[ADD]: four color theorem works for every planar graph and it looks like one can make such graph corresponding to any convex polyhedron, so it seems that original OP statement holds.

The second advantage is power: if you have proved \n something about regular polyhedra, then what you \n have proved automatically holds true for every \n polyhedron, whether it's a cube, a tetrahedron, or \n some polyhedron that you have never even heard about.\n\nIs this worded correctly/true?