I think the formula for the number of foldable tessellation possible given a specific grid (m x n): (m^(2mn-m-n))(n^(2mn-m-mn)) Additionally foldable tessellations can be composed of units with identical geometric patterns that are tessellated. Another option, which involves geometric gradients:

Degree 3 shapes intersect the x-axis at a maximum of three points

2D crystallographic symmetry is a way of describing patterns of symmetry in two-dimensional crystalline structures. A crystalline is a solid material with a highly ordered microscopic structure. At a larger scale, crystalline structures could also be tiles or wallpapers – patterns that repeat in a...

Some potential computational/geometrical Miura-Ori related research prompts:

The Miura Ori tessellation is recognized for having unique properties, one of which is its negative Poisson’s ratio. The Poisson’s ratio is the ratio of how much a material contracts or extends in the transversal and longitudinal direction, when subject to a tensile force. Most...

Developed by Biruta Kresling, Paris-based architect and researcher on folded structures. The pattern is the result of the natural warping of paper from torsional load. Kresling shows how this warping could be used through an experiment with cylinders and paper. She found that after wrapping...

Expanding from conventional figurative designs to investigating mathematical properties. Barreto’s ‘Mars’. Mountain folds are indicated by solid lines and valley folds by dashed lines. Fold lines of the same colour have the same fold angle. (a) Fold pattern, (b) partially folded position, and (c) mostly...

It is made from standard paper glued to thin copper sheets. The resulted material is 0.25 mm thick, and is folded into water bomb bases, which interlock with each other, forming a tetrahedron. There is also a reflector and two strip detectors, both of which...

The Maekawa Theorem, named after Jun Maekawa, tells us that in flat-folded origami, the difference between the number of mountain and valley creases at any vertex is always two. This is what enables origami pieces to be flattened. To visualize this principle, one can unfold...