Hexagonal bipyramid bipyramid has a plane of symmetry (which is horizontal in the figure to the right) where the bases of the two pyramids are joined. This plane is a regular hexagon. There are also six planes of symmetry crossing through the two apices. These planes are rhombic and lie at 30° angles to each other, perpendicular to the horizontal plane. It can be drawn as a tiling on a sphere which also represents the fundamental domains of [3,2], *322 dihedral symmetry: The hexagonal bipyramid, dt{2,6}, can be in sequence truncated, tdt{2,6} and alternated (snubbed), sdt{2,6}: The "hexagonal bipyramid", dt{2,6}, can be
Mathematics and art mathematically. Islamic art exploits symmetries in many of its artforms, notably in girih tilings. These are formed using a set of five tile shapes, namely a regular decagon, an elongated hexagon, a bow tie, a rhombus, and a regular pentagon. All the sides of these tiles have the same length; and all their angles are multiples of 36° (π/5 radians), offering fivefold and tenfold symmetries. The tiles are decorated with strapwork lines (girih), generally more visible than the tile boundaries. In 2007, the physicists Peter Lu and Paul Steinhardt argued that girih resembled quasicrystalline Penrose tilings. Elaborate geometric zellige tilework