42 research outputs found
Rotationally symmetric tilings with convex pentagons belonging to both the Type 1 and Type 7
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 rotational symmetry. Those rotationally symmetric
tilings are connected edge-to-edge and have no axis of reflection symmetry.Comment: 13 pages, 16 figures. arXiv admin note: text overlap with
arXiv:2005.08470, arXiv:2005.1270
Convex pentagons and convex hexagons that can form rotationally symmetric tilings
In this study, the properties of convex hexagons that can generate
rotationally symmetric edge-to-edge tilings are discussed. Since the convex
hexagons are equilateral convex parallelohexagons, convex pentagons generated
by bisecting the hexagons can form rotationally symmetric non-edge-to-edge
tilings. In addition, under certain circumstances, tiling-like patterns with an
equilateral convex polygonal hole at the center can be formed using these
convex hexagons or pentagons.Comment: 23 pages, 28 figures. arXiv admin note: text overlap with
arXiv:2005.0847
Pentagons and rhombuses that can form rotationally symmetric tilings
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 be degenerated into a trapezoid. If the pentagons are
convex, they belong to the Type 2 family. Since the properties of pentagons
correspond to those of rhombuses, the study also explains the correspondence
between pentagons and various rhombic tilings.Comment: 50 pages, 42 figure
Pentagonal Tilings of the Plane
Tilings are mathematical objects that allow us to use geometry to visualize interaction between objects as well as to create artistic realization of mathematical objects in the plane and in the space.
We will focus on tilings of the plane that use only one type of convex pentagonal tile each, the pentagonal tilings. There are fifteen types of pentagonal tiles, with each containing their own set of restrictions. The main result of this thesis is an interactive realization of all fifteen types of pentagonal tiles using GeoGebra