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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“With our principles we seek to rule our habits with an iron hand, or to justify, honor, scold, or conceal them:Mtwo men with identical principles are likely to be seeking fundamentally different things with them.”
—Friedrich Nietzsche (1844–1900)