Ribbon Tilings From Spherical Ones
نویسنده
چکیده
The problem of classifying all tile-k-transitive tilings of the innnite 2-dimensional ribbon (and pinched-ribbon) is shown to be solvable by classifying certain tile-k-transitive tilings of the sphere, for all k 2 N. Complete results are listed for k 3.
منابع مشابه
Ribbon Tilings and Multidimensional Height Functions
We fix n and say a square in the two-dimensional grid indexed by (x, y) has color c if x+ y ≡ c (mod n). A ribbon tile of order-n is a connected polyomino containing exactly one square of each color. We show that the set of order-n ribbon tilings of a simply connected region R is in one-to-one correspondence with a set of height functions from the vertices of R to Zn satisfying certain differen...
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 کاملPolyominoes simulating arbitrary-neighborhood zippers and tilings
This paper provides a bridge between the classical tiling theory and cellular automata on one side, and the complex neighborhood self-assembling situations that exist in practice, on the other side. A neighborhood N is a finite set of pairs (i, j) ∈ Z, indicating that the neighbors of a position (x, y) are the positions (x + i, y + j) for (i, j) ∈ N . This includes classical neighborhoods of si...
متن کاملRight Triangular Spherical Dihedral f–Tilings with Two Pairs of Congruent Sides
By a dihedral folding tiling (f-tiling, for short) of the sphere S whose prototiles are spherical right triangles, T1 and T2, we mean a polygonal subdivision τ of S such that each cell (tile) of τ is congruent to T1 or T2 and the vertices of τ satisfy the angle-folding relation, i.e., each vertex of τ is of even valency and the sums of alternating angles around each vertex are π. In fact, the c...
متن کاملSpherical f-Tilings by Scalene Triangles and Isosceles Trapezoids III
The study of the dihedral f-tilings of the sphere S2 whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in [7, 8]. In this paper we complete this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in the remaining case of adjacency. A list containing all the f-tilings obtained in this paper is prese...
متن کامل