Hexagonal Tiling - Topologically Identical Tilings

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.

4-color hexagonal tilings
Regular hexagons Hexagonal weave
p6m (*632) p6 (632)
Brick pattern Herringbone
p4g (4*2)
|

Read more about this topic:  Hexagonal Tiling

Famous quotes containing the word identical:

    It is hard to believe that England is so near as from your letters it appears; and that this identical piece of paper has lately come all the way from there hither, begrimed with the English dust which made you hesitate to use it; from England, which is only historical fairyland to me, to America, which I have put my spade into, and about which there is no doubt.
    Henry David Thoreau (1817–1862)