Teruhisa Sugimoto
For a long time, tessellation (tiling), covering, and packing have fascinated me. Especially tessellations by convex pentagons have a relationship with roughly half of my life. The time I have been doing mathematical exploration so far was long, but artistic curiosity was always in me. In recent years, I spend a lot of time on artistic activities.
The convex pentagon in the model includes 7/3 equilateral
triangles, and is a unique convex pentagon obtained from a
trisected heptiamond (TH). This convex pentagon has been termed as
a “TH-pentagon” by the associated authors. TH-pentagons can form
hexagonal flowers of three different sizes. A small hexagonal
flower comprises 18 TH-pentagons, with a single unique pattern. A
medium hexagonal flower consists of 72 TH-pentagons and possesses
15 unique patterns. A large hexagonal flower comprises 162
TH-pentagons, along with two unique patterns. The TH-pentagon can
create infinite patterns of tessellation.
In the proposed model, players are challenged to fill the frame of
each hexagonal flower by using pieces that are shaped as
TH-pentagons.