1 citations · 3 across the 17 of their papers we have counts for
17 papers
Tile sets consisting of two types of concave polygons derived from periodic tilings corresponding to non-periodic tilings with hat and turtle tiles
Teruhisa Sugimoto
Using a convex pentagonal monotile belonging to the Type 5 family, we investigate the relationships among the hat tile, turtle tile, and Tile. By applying Sugimoto's Perspe…
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.
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…
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…
Converting tilings with multiple types of rhombuses to pentagonal tilings
Teruhisa Sugimoto
The results involving rotationally symmetric tilings with multiple types of rhombuses, discovered by Penrose, Ammann, Beenker, or Socolar, are converted to tilings with multiple ty…
Rotationally symmetric tilings with convex pentagons belonging to both the Type 1 and Type 7 families
Teruhisa Sugimoto
Rotationally symmetric tilings by a convex pentagonal tile belonging to both the Type 1 and Type 7 families are introduced. Among them are spiral tilings with two- and four-fold ro…
Pentagons and rhombuses that can form rotationally symmetric tilings
Teruhisa Sugimoto
In this study, various rotationally symmetric tilings that can be formed using pentagons that are related to rhombus are discussed. The pentagons can be convex or concave and can b…
Convex pentagons and convex hexagons that can form rotationally symmetric tilings
Teruhisa Sugimoto
In this study, the properties of convex hexagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the convex hexagons are equilateral convex paralle…
Convex pentagons and concave octagons that can form rotationally symmetric tilings
Teruhisa Sugimoto
In this study, the properties of convex pentagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the rotationally symmetric tilings are formed by…
Properties of Convex Pentagonal Tiles for Periodic Tiling
Teruhisa Sugimoto
A convex pentagonal tile is a convex pentagon that admits a monohedral tiling. We show that a convex pentagonal tile that admits a periodic tiling has a property in which the sum o…
Convex Pentagons with Positive Heesch Number
Teruhisa Sugimoto
We found convex pentagons whose Heesch number is equal to one, and which admit an edge-to-edge corona. In this manuscript, we present a new classification of these convex pentagons…
Convex Pentagon Tilings and Heptiamonds, II
Teruhisa Sugimoto, Yoshiaki Araki
In the previous manuscript, new tilings (tessellations) were presented using convex pentagonal tiles belonging to Type 1 and Type 5. The convex pentagon tilings are related to hept…
Convex Pentagon Tilings and Heptiamonds, I
Teruhisa Sugimoto, Yoshiaki Araki
In 1995, Marjorie Rice discovered an interesting tiling by using convex pentagons. The authors discovered novel properties of the tilings of convex pentagon which Rice used in the…
Properties of Strongly Balanced Tilings by Convex Polygons
Teruhisa Sugimoto
Every normal periodic tiling is a strongly balanced tiling. The properties of periodic tilings by convex polygons are rearranged from the knowledge of strongly balanced tilings. Fr…
Convex Polygons for Aperiodic Tiling
Teruhisa Sugimoto
If all tiles in a tiling are congruent, the tiling is called monohedral. Tiling by convex polygons is called edge-to-edge if any two convex polygons are either disjoint or share on…
Exact value of Tammes problem for N=10
Teruhisa Sugimoto, Masaharu Tanemura
Let () be the -th open spherical cap of angular radius and let be its center under the condition that none of the spherical caps contains…
Tiling Problem: Convex Pentagons for Edge-to-Edge Monohedral Tiling and Convex Polygons for Aperiodic Tiling
Teruhisa Sugimoto
We show that convex pentagons that can generate edge-to-edge monohedral tilings of the plane can be classified into exactly eight types. Using these results, it is also proved that…