Octagon tessellation12/15/2023 ![]() Such a hexagon would lie on a plane consisting of all points with coordinates that add up to 6, and would bisect a cube of unit length 2 between coordinates 1 and 3.Īnother interesting thing about hexagons-and perhaps the most striking fact about them-is that they do, in fact, have six sides. ![]() Hexagons are third-order permutohedra, meaning each vertex of a hexagon can be described with Cartesian coordinates using one of six permutations of the numbers 1, 2, and 3.A consequence of this is that no regular polytope, in any dimension, has hexagonal faces-though many have hexagon-like or hexagonally-symmetric vertices or other elements. The three polygons with fewer sides compose the surfaces of the five platonic solids, but no polygon with six or more sides can be employed for this purpose. ![]()
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