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  2. Hexagon - Wikipedia

    en.wikipedia.org/wiki/Hexagon

    A regular hexagon has Schläfli symbol {6} [2] and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an ...

  3. List of Euclidean uniform tilings - Wikipedia

    en.wikipedia.org/wiki/List_of_euclidean_uniform...

    The Laves tilings have vertices at the centers of the regular polygons, and edges connecting centers of regular polygons that share an edge. The tiles of the Laves tilings are called planigons. This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it.

  4. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms;

  5. Euclidean tilings by convex regular polygons - Wikipedia

    en.wikipedia.org/wiki/Euclidean_tilings_by...

    This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling.

  6. Hexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_tiling

    In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t{3,6} (as a truncated triangular tiling).

  7. Truncated hexagonal trapezohedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_hexagonal...

    The Weaire–Phelan structure contains another form of this polyhedron that has D 2d symmetry and is a part of a space-filling honeycomb along with an irregular dodecahedron. Irregular tetradecahedron

  8. Icositetragon - Wikipedia

    en.wikipedia.org/wiki/Icositetragon

    In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular icositetragon, m=12, and it can be divided into 66: 6 squares and 5 sets of 12 rhombs. This decomposition is based on a Petrie polygon projection of a 12-cube.

  9. Truncated hexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Truncated_hexagonal_tiling

    In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.There are 2 dodecagons (12-sides) and one triangle on each vertex.. As the name implies this tiling is constructed by a truncation operation applied to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations.