TY  - JOUR
AB  - Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a single prototile with nearest neighbour matching rules, which is then called a monotile. One strand of the search for a planar monotile has focused on hexagonal analogues of Wang tiles. This led to two inflation tilings with interesting structural details. Both possess aperiodic local rules that define hulls with a model set structure. We review them in comparison, and clarify their relation with the classic half-hex tiling. In particular, we formulate various known results in a more comparative way, and augment them with some new results on the geometry and the topology of the underlying tiling spaces.
DA  - 2012
DO  - 10.3390/sym4040581
LA  - eng
IS  - 4
M2  - 581
PY  - 2012
SN  - 2073-8994
SP  - 581-602
T2  - Symmetry
TI  - Hexagonal Inflation Tilings and Planar Monotiles
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-25412972
Y2  - 2024-12-04T08:41:42
ER  -