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  2. Polyhex (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Polyhex_(mathematics)

    One example self-tiling with a pentahex. All of the polyhexes with fewer than five hexagons can form at least one regular plane tiling. In addition, the plane tilings of the dihex and straight polyhexes are invariant under 180 degrees rotation or reflection parallel or perpendicular to the long axis of the dihex (order 2 rotational and order 4 reflection symmetry), and the hexagon tiling and ...

  3. Hexagon - Wikipedia

    en.wikipedia.org/wiki/Hexagon

    Full symmetry of the regular form is r12 and no symmetry is labeled a1. The regular hexagon has D 6 symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D 6), 2 dihedral: (D 3, D 2), 4 cyclic: (Z 6, Z 3, Z 2, Z 1) and the trivial (e) These symmetries express nine distinct symmetries of a regular hexagon.

  4. List of two-dimensional geometric shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_two-dimensional...

    This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.

  5. Elongated hexagonal bipyramid - Wikipedia

    en.wikipedia.org/wiki/Elongated_hexagonal_bipyramid

    This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solids: J 14, J 15, and J 16.The hexagonal form can be constructed by all regular faces but is not a Johnson solid because 6 equilateral triangles would form six co-planar faces (in a regular hexagon).

  6. Hexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_tiling

    Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.

  7. Hexagonal prism - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_prism

    Alternately it can be seen as the Cartesian product of a regular hexagon and a line segment, and represented by the product {6}×{}. The dual of a hexagonal prism is a hexagonal bipyramid. The symmetry group of a right hexagonal prism is D 6h of order 24. The rotation group is D 6 of order 12.

  8. Elongated dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Elongated_dodecahedron

    3D model of a elongated dodecahedron. In geometry, the elongated dodecahedron, [1] extended rhombic dodecahedron, rhombo-hexagonal dodecahedron [2] or hexarhombic dodecahedron [3] is a convex dodecahedron with 8 rhombic and 4 hexagonal faces.

  9. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    6 hexagons around each vertex: {6,6|3} 12 3-dimensional "pure" apeirohedra based on the structure of the cubic honeycomb , {4,3,4}. [ 22 ] A π petrie dual operator replaces faces with petrie polygons ; δ is a dual operator reverses vertices and faces; φ k is a k th facetting operator; η is a halving operator, and σ skewing halving operator.