Today's new Wikipedia articles: Hanner polytopes and Kalai's $$3^d$$ conjecture.

The $$3^d$$ conjecture states that a centrally symmetric $$d$$-dimensional polytope must have at least $$3^d$$ faces (of all dimensions including the $$d$$-dimensional polytope itself as a face but not including the $$-1$$-dimensional empty set). For instance, the cube has $$8$$ vertices, $$12$$ edges, $$6$$ squares, and $$1$$ cube as faces; $$8 + 12 + 6 + 1 = 27 = 3^3.$$

The Hanner polytopes include the cubes, are closed under Cartesian products and duality, and if the conjecture is true have the fewest possible numbers of faces of all centrally symmetric $$d$$-dimensional polytopes. They also have some other interesting properties. In 3d there are only the cube and the octahedron, but in higher dimensions there are a lot more of them.