Topologically Identical Tilings
The hexagonal tiling can be stretched and adjusted to other geometric proportions and different symmetries.
The standard brick pattern can be considered a nonregular hexagonal tiling. Each rectangular brick has vertices inserted on the two long edges, dividing them into two collinear edges.
It can also be distorted into a chiral 4-colored tri-directional weaved pattern, distorting some hexagons into parallelograms. The weaved pattern with 4-colored faces have rotational 632 (p6) symmetry. The herringbone pattern is also a distorted hexagonal tiling.
| Regular hexagons | Hexagonal weave |
|---|---|
| p6m (*632) | p6 (632) |
| Brick pattern | Herringbone |
| p4g (4*2) | |
| | | |
Read more about this topic: Hexagonal Tiling
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“But the life of Spirit is not the life that shrinks from death and keeps itself untouched by devastation, but rather the life that endures it and maintains itself in it. It wins its truth only when, in utter dismemberment, it finds itself.... Spirit is this power only by looking the negative in the face, and tarrying with it. This tarrying with the negative is the magical power that converts it into being. This power is identical with what we earlier called the Subject.”
—Georg Wilhelm Friedrich Hegel (1770–1831)