18 citations · 43 across the 10 of their papers we have counts for
4 papers · 1 filter
Fair partitions of the plane into incongruent pentagons
Dirk Frettlöh, Christian Richter
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex pentagons of the same area and the same perimeter.
Incongruent equipartitions of the plane into quadrangles of equal perimeter
Dirk Frettlöh, Christian Richter
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. A…
Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary
Dirk Frettlöh, Alexey Garber
This paper uses a connection between bounded remainder sets in and cut-and-project sets in together with the fact that each one-dimensional Pisot substi…
Substitution tilings with dense tile orientations and n-fold rotational symmetry
Dirk Frettlöh, April L. D. Say-awen, M. L. A. N. de las Peñas
It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n=2,3,4,5,6,8. The proof for dense tile orientations uses…