The 12-fold tiles easily tile periodically, so special rules are defined to limit their connections and force nonperiodic tilings. The rhombus and square are disallowed from touching another of itself, while the hexagon can connect to both tiles as well as itself, but only in alternate edges.
Dodecagonal rhomb tilingedit
The dodecagonal rhomb tiling include three tiles, a 30° rhombus, a 60° rhombus, and a square.[3] And expanded set can also include an equilateral triangle, half of the 60° rhombus.60° rhombus.[4]
See alsoedit
Pattern block - 6 tiles based on 12-fold symmetry, including the 3 Socolar tiles
socolar, tiling, there, socolar, tile, rhombus, square, regular, hexagon, with, tiling, rules, defined, fins, rules, tiling, fill, regular, dodecagon, example, aperiodic, tiling, developed, 1989, joshua, socolar, exploration, quasicrystals, there, tiles, rhomb. There are 3 Socolar tile a 30 rhombus square and a regular hexagon with tiling rules defined by the fins The rules of tiling can fill a regular dodecagon A Socolar tiling is an example of an aperiodic tiling developed in 1989 by Joshua Socolar in the exploration of quasicrystals 1 There are 3 tiles a 30 rhombus square and regular hexagon The 12 fold symmetry set exist similar to the 10 fold Penrose rhombic tilings and 8 fold Ammann Beenker tilings 2 Pattern blocks contain the 3 tiles and 3 more The 12 fold tiles easily tile periodically so special rules are defined to limit their connections and force nonperiodic tilings The rhombus and square are disallowed from touching another of itself while the hexagon can connect to both tiles as well as itself but only in alternate edges Dodecagonal rhomb tiling editThe dodecagonal rhomb tiling include three tiles a 30 rhombus a 60 rhombus and a square 3 And expanded set can also include an equilateral triangle half of the 60 rhombus 60 rhombus 4 See also editPattern block 6 tiles based on 12 fold symmetry including the 3 Socolar tiles Socolar Taylor tile A different tiling named after SocolarReferences edit Socolar Joshua E S 1989 Simple octagonal and dodecagonal quasicrystals Physical Review B 39 15 10519 51 Bibcode 1989PhRvB 3910519S doi 10 1103 PhysRevB 39 10519 PMID 9947860 Tilings Encyclopedia Socolar Crystallography of Quasicrystals Concepts Methods and Structures By Steurer Walter Sofia Deloudi pp 40 41 1 A Quasiperiodic Tiling With 12 Fold Rotational Symmetry and Inflation Factor 1 3 Theo P Schaad and Peter Stampfli 10 Feb 2021 nbsp This geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Socolar tiling amp oldid 1223561475, wikipedia, wiki, book, books, library,
