Chasing rotational symmetry in the spectre tiling

RESUMO

We identify the rotational symmetry centers in the spectre tiling. We find that both 2-fold and 3-fold symmetry centers are coexisting. Local and global symmetry operations are distinguished. The link between substitution schemes and rotational symmetry is investigated. We introduce a set of three finite patterns, named diabolo, 2-arms and 3-arms, in order to visualize rotational symmetry in the spectre tiling. Using these three patterns, we propose geometrical constructions for generating patches of the spectre tiling with 2-fold and 3-fold global rotational symmetry.