Tom Lindquist
I have been interested in both math and origami from a young age, and
recently I have been interested in the world of origami tessellations.
These tessellations are mathematically interesting, allowing for many
different types of tiling and symmetry, as well as technically
interesting to design and fold, and the final product is visually
pleasing. I have been especially fond of tessellations with a
three-dimensional aspect to them, although I also enjoy a technique
known as "flagstone tessellation" which creates a flat tiling of
polygons, generally hexagons, triangles, rhombi and trapezoids.
With this tessellation, I wanted to explore the possibility of
creating an origami tessellation based on an aperiodic tiling. It
shows the Penrose P3 tiling, using two types of rhombi, which are
only allowed to match together in particular ways. This was my
first time attempting something like this, so I used a very simple
tessellation technique, where the vertices of the tiling are
formed by twists on the back of the paper, creating a "weaving"
effect. The difficulty in designing this was in creating twists in
the paper that produce the 8 desired vertex figures. In order for
these twists to lie flat, they produce pleat widths related by the
golden ratio, although this beautiful fact is not visible on the
front of the tessellation.