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.
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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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