Interesting tiling with a lot of symmetrical shapes

reference-request quadrilateral symmetry tessellations tiling

Such kind of things are called multi-grids. The kind of multi-grids you drew are called singular. Non-singular or regular multi-grids, where no three different lines intersect, provide a general method for constructing non-periodic tilings of the plane. They were used (maybe itroduced?) by N. de Bruijn in his paper Algebraic theory of Penrose tilings. Later on de Bruijn's student Beenker used tetra-grids to describe Ammann-Beenker tilings -take a look at references therein.

The multi-grids method for constructing non-periodic tilings of the plane is generalized by the projection method (also cut-and-project method) and is related to the mathematical theory of quasi-crystals. Such method consists in projecting a stripe of a higher dimensional lattice onto a totally irrational subspace.

The relation between projection tilings and the inflational structure was studied by Harriss and Lamb.

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