Lattice Labyrinth Tessellations rarely (and inconsequentially so far as I’m concerned) exhibit mirror symmetry, that is they don’t look the same if you reflect them or flip them over to look from the other side. They are right- or left-handed you might say – which to most of us means asymmetrical. They do however exhibit beautiful rotational symmetry. Here are some flower-petal patterns that illustrate what I mean and the symbols that are used to illustrate rotational symmetry properties.
The chessboard or square lattice tessellations exhibit patterns of symmetry axes. They also exhibit mirror symmetry, but let’s ignore that to avoid complicating the picture – only the rotational symmetry is inherited by Lattice Labyrinths tessellations.
The tetrad axes are marked in two colours as the red and black axes have different environments, the centres and corners of squares respectively. The dyad axes appear in differing orientations because that’s how they are inter-related by the tetrad and hexad or triad axes, around with they “swing”. If you now return to some of the other posts, you can see how they (so far, there will be others) share one or other of these patterns of rotational symmetry axes.
LatticeLabyrinths 