Hexagonal tiles split in half in two ways. Metrorail station floor, Washington, D.C.
Dividing a hexagonal tile in half from vertex to vertex produces a pair of identical quadrilaterals, which tile the plane; dividing a hexagonal tile in half from side to side produces a pair of identical pentagons, which also tile the plane.
For more on hexagonal tiles in Metrorail stations, see "From Hexagon to Square." See also "Tiling with Pentagons" and "Hexatiles."
Photos by I. Peterson