Square Tiling - Quadrilateral Tiling Variations

Quadrilateral Tiling Variations

Quadrilateral tilings can be made with the identical {4,4} topology as the square tiling (4 quads around every vertex). With identical faces (face-transitivity) and vertex-transitivity, there are 17 variations, with the first 6 identified as triangles that don't connect edge-to-edge, or as quadrilateral with two colinear edges. Symmetry given assumes all faces are the same color.

  • Scalene triangle
    p2 symmetry

  • Scalene triangle
    pgg symmetry

  • Isosceles triangle
    pgg symmetry

  • Isosceles triangle
    pgg symmetry

  • Scalene triangle
    pgg symmetry

  • Isosceles triangle
    pmg symmetry

  • Quadrilateral
    p2 symmetry

  • Quadrilateral
    pgg symmetry

  • Kite
    pmg symmetry

  • Rhombus
    cmm symmetry

  • Parallelogram
    p2 symmetry

  • Parallelogram
    pmg symmetry

  • Quadrilateral
    pgg symmetry

  • Trapezoid
    cmm symmetry

  • (Half regular hexagon)
    Trapezoid
    cmm symmetry

  • Rectangle
    pmm symmetry

  • Square
    p4m symmetry

Read more about this topic:  Square Tiling

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