Some Monohedral Tilings Derived From Regular Polygons
نویسنده
چکیده
Some tiles derived from regular polygons can produce spiral tilings of the plane [1]. This paper considers some more general classes of tilings with tiles derived from regular polygons, some have central symmetry, many have periodic symmetry, some have both, and a few have no symmetry at all. Any of these tiling patterns could be the basis for some interesting mathematical art, for example by colouring or decorating the tiles.
منابع مشابه
Tiling with Regular Star Polygons
The Archimedean tilings (Figure 1) and polyhedra will be familiar to many readers. They have the property that the tiles of the tiling, or the faces of the polyhedron, are regular polygons, and that the vertices form a single orbit under the symmetries of the tiling or polyhedron. (Grünbaum and Shephard [1] use Archimedean, in relation to tilings, to refer to the sequence of polygons at each ve...
متن کاملInfinite families of monohedral disk tilings
A tiling of a planar shape is called monohedral if all tiles are congruent to each other. We will investigate the possibility of producing monohedral tilings of the disk. Such tilings are produced on a daily basis by pizza chefs by taking radial cuts distributed evenly around the centre of the pizza. After constructing this tiling, a neighbourhood of the origin has non-trivial intersection with...
متن کاملTilings by Regular Polygons Iii: Dodecagon-dense Tilings
In Tilings and Patterns, Grünbaum and Shephard claim that there are only four kuniform tilings by regular polygons (for some k) that have a dodecagon incident at every vertex. In fact, there are many others. We show that the tilings that satisfy this requirement are either the uniform 4.6.12 tiling, or else fall into one of two infinite classes of such tilings. One of these infinite classes can...
متن کاملDihedral f-tilings of the sphere by rhombi and triangles
An isometric folding is a non-expansive locally isometry that sends piecewise geodesic segments into piecewise geodesic segments of the same length. An isometric folding is a continuous map that need not to be differentiable. The points where it is not differentiable are called singular points. The foundations of isometric foldings of Riemannian manifolds are introduced by Robertson (1977). For...
متن کاملSpherical F-Tilings by Triangles and r-Sided Regular Polygons, r >= 5
The study of dihedral f-tilings of the sphere S2 by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented in [3]. Also, in [6], the study of dihedral f-tilings of S2 whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scal...
متن کامل