3 papers
math.HO2026
Convex pentagonal monotiles in the 15 Type families
Teruhisa Sugimoto
The properties of convex pentagonal monotiles in the 15 Type families and their tilings are summarized. The Venn diagrams of the 15 Type families are also shown.
math.MG2025
Converting non-periodic tilings with Tile(1, 1) into tilings with three types of pentagons, I
Teruhisa Sugimoto
Non-periodic tilings with Tile(1, 1) using the substitution method, as presented by Smith et al. in [2] and [3], can be converted into non-periodic tilings with three types of pent…
math.MG2025
Aperiodic sets of three types of convex polygons
Teruhisa Sugimoto
Sets of three types of convex pentagons that are aperiodic with no matching conditions on the edges are created from a chiral aperiodic monotile Tile(1, 1). This method divides the…