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  2. Hexagon - Wikipedia

    en.wikipedia.org/wiki/Hexagon

    A regular skew hexagon seen as edges (black) of a triangular antiprism, symmetry D 3d, [2 +,6], (2*3), order 12. A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such a hexagon is not generally defined. A skew zig-zag hexagon has vertices alternating between two parallel planes.

  3. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of ⁠ ⁠ (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...

  4. Hermann–Mauguin notation - Wikipedia

    en.wikipedia.org/wiki/Hermann–Mauguin_notation

    This can be done if the rotation axis can be unambiguously obtained from the combination of symmetry elements presented in the symbol. For example, the short symbol for ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ is mmm, for ⁠ 4 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ is ⁠ 4 / m ⁠ mm, and for ⁠ 4 / m ⁠ 3 ⁠ 2 / m ⁠ is m 3 m.

  5. List of planar symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_planar_symmetry_groups

    This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...

  6. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    A rhombus has an inscribed circle, while a rectangle has a circumcircle. A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides. The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.

  7. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon.

  8. Hexagonal lattice - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_lattice

    The gray rhombus is a primitive cell. Vectors a 1 {\displaystyle \mathbf {a} _{1}} and a 2 {\displaystyle \mathbf {a} _{2}} are primitive translation vectors. The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [ 1 ]

  9. Rhombitrihexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Rhombitrihexagonal_tiling

    Point symmetry allows the plane to be filled by growing kites, with the topology as a square tiling, V4.4.4.4, and can be created by crossing string of a dream catcher. Below is an example with dihedral hexagonal symmetry.