Rhombic tilings and Bott–Samelson varieties

Rhombic Tilings and Primordia Fronts of Phyllotaxis

We introduce and study properties of phyllotactic and rhombic tilings on the cylinder. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, a...

Rhombic Penrose Tilings Can be 3-Colored

Rhombic Tilings of Polygons and Classes of Reduced Words in Coxeter Groups

In the standard Coxeter presentation, the symmetric group Sn is generated by the ad jacent transpositions (1,2), (2,3), ... , (n1,n). For any given permutation, we consider all minimal-length factorizations thereof as a product of the generators. Any two transpositions (i,i+1) and (j,j+1) commute if the numbers i and j are not consecutive; thus, in any factorization, their order can be switche...

Ferroelectric hexagonal and rhombic monolayer ice phases

Quaquaversal Tilings and Rotations

We construct a hierarchical tiling of 3 dimensional Euclidean space based on a triangular prism, using repeated rotations, about orthogonal axes, by angles 2=m and 2=n. To analyze the structure of the tiling we are led to determine the group G(m; n) generated by such a pair of rotations, for m = n = 3 and for m = 3; n = 4.