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  2. Euclidean tilings by convex regular polygons - Wikipedia

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

    1-uniform tilings include 3 regular tilings, and 8 semiregular ones, with 2 or more types of regular polygon faces. There are 20 2-uniform tilings, 61 3-uniform tilings, 151 4-uniform tilings, 332 5-uniform tilings and 673 6-uniform tilings. Each can be grouped by the number m of distinct vertex figures, which are also called m-Archimedean tilings.

  3. Digon - Wikipedia

    en.wikipedia.org/wiki/Digon

    In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space .

  4. Vertex configuration - Wikipedia

    en.wikipedia.org/wiki/Vertex_configuration

    In geometry, a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex.It has variously been called a vertex description, [1] [2] [3] vertex type, [4] [5] vertex symbol, [6] [7] vertex arrangement, [8] vertex pattern, [9] face-vector, [10] vertex sequence. [11]

  5. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    [2]: p. 1 They could also construct half of a given angle, a square whose area is twice that of another square, a square having the same area as a given polygon, and regular polygons of 3, 4, or 5 sides [2]: p. xi (or one with twice the number of sides of a given polygon [2]: pp. 49–50 ).

  6. Uniform tiling - Wikipedia

    en.wikipedia.org/wiki/Uniform_tiling

    Tilings 3.7 through 3.10 have the same edge arrangement as 2.1 and 2.2; 3.17 through 3.20 have the same edge arrangement as 2.10 through 2.13; 3.21 through 3.24 have the same edge arrangement as 2.18 through 2.23; and 3.25 through 3.33 have the same edge arrangement as 1.25 (the regular triangular tiling). [2]

  7. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.

  8. Translation surface - Wikipedia

    en.wikipedia.org/wiki/Translation_surface

    In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form. These surfaces arise in dynamical systems where they can be used to model billiards, and in Teichmüller theory.

  9. Incidence geometry - Wikipedia

    en.wikipedia.org/wiki/Incidence_geometry

    Given an integer α ≥ 1, a tactical configuration satisfying: For every anti-flag (B, m) there are α flags (A, l) such that B I l and A I m, is called a partial geometry. If there are s + 1 points on a line and t + 1 lines through a point, the notation for a partial geometry is pg(s, t, α). If α = 1 these partial geometries are generalized ...