Various Kawasaki Rose Tessellations:

Square twist roses in a square array:

Look at what this model does as you flex it ... spontaneous Gaussian curvature, and aPoisson ratio of -1 !  Can you see the hyperbolic paraboloid that appears all by itself?

A seven-rose cluster with folding instructions:

and Smoke:

``Triangle'' roses on a honeycomb lattice
Anti-symmetric version (each rose is surrounded by roses twisting in the opposite direction):

antiferromagnet honeycomb

Symmetric version (each rose is twisting the same way)
ferromagnetic honeycomb

``Hexagon'' roses on a triangle lattice.  There is no anti-symmetric version, this is related to the fact that an antiferromagnet on a triangle lattice is frustrated!
ferromagnetic_triangular
and another version:

Square roses with a domain wall:  the red half of the picture and the blue half spin around in opposite directions:
domain wall defect

Two columns of square twist roses: notice the repeating heart motif going down the center:
row of hearts

The row of hearts expanded so you can get an idea of the crease pattern:
hearts crease pattern

A self-similar set of growing square twist roses:
self-similar roses

A 4x6 array of symmetric roses, folded from 12x18 drawing paper decorated with oil pastel.
4 by 6 Kawasaki array

An array of squares and octagons, held together exclusively by traingle (not equilateral, however) twist roses:
  and the back: