Hexagon side of any hexagon, then the midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle. A skew hexagon is a skew polygon with 6 vertices and edges but not existing on the same plane. The interior of such an hexagon is not generally defined. A "skew zig-zag hexagon" has vertices alternating between two parallel planes. A regular skew hexagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew hexagon and can be seen in the vertices and side edges of a triangular antiprism with the same D, [2,6] symmetry, order
Magic hexagon gave a less intricate constructive proof. The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887). The numbers in the hexagon are consecutive, and run from 1 to formula_1. Hence their sum is a triangular number, namely There are "r" = (2"n" − 1) rows running along any given direction (E-W, NE-SW, or NW-SE). Each of these rows sum up to the same number "M". Therefore: This can be rewritten as Multiplying throughout by 32 gives which shows that formula_6 must be an integer,