Geometric Relations
A cube has eleven nets (one shown above): that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the same color, one would need at least three colors.
The cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the Platonic solids in having faces with an even number of sides and, consequently, it is the only member of that group that is a zonohedron (every face has point symmetry).
The cube can be cut into six identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces.)
Read more about this topic: Cube
Famous quotes containing the words geometric and/or relations:
“New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”
—Roland Barthes (1915–1980)
“So soon did we, wayfarers, begin to learn that man’s life is rounded with the same few facts, the same simple relations everywhere, and it is vain to travel to find it new.”
—Henry David Thoreau (1817–1862)