23 citations · 24 across the 9 of their papers we have counts for
11 papers
Frieze patterns and aperiodic tilings of the plane
Dirk Frettlöh, Jan Mazáč
This short note provides two examples of aperiodic frieze patterns of the plane, supported on the rhombic Penrose tiling and the Godrèche--Lançon--Billard tiling. That is, we provi…
Bounded Displacement Non-Equivalence In Substitution Tilings
Dirk Frettlöh, Yotam Smilansky, Yaar Solomon
In the study of aperiodic order and mathematical models of quasicrystals, questions regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the bo…
Incongruent equipartitions of the plane
Dirk Frettlöh, Christian Richter
R. Nandakumar asked whether there is a tiling of the plane by pairwise incongruent triangles of equal area and equal perimeter. Recently a negative answer was given by Kupavskii, P…
Fundamental domains for rhombic lattices with dihedral symmetry of order 8
Joseph Ray Clarence G. Damasco, Dirk Frettlöh, Manuel Joseph C. Loquias
We show by construction that every rhombic lattice in has a fundamental domain whose symmetry group contains the point group of as a subgroup of index .…
Inductive Rotation Tilings
Dirk Frettlöh, Kurt Hofstetter
A new method for constructing aperiodic tilings is presented. The method is illustrated by constructing a particular tiling and its hull. The properties of this tiling and the hull…
On Bravais colourings of cyclotomic integers with class number one
Enrico Paolo Bugarin
Given a Bravais colouring of planar modules $\M_n:=\Z[ξ_n]$, where is a primitive th root of unity, two important colour groups arise: the colour symmetry group , which…