Title : The formation of the four-way symmetric translational tiles (crystal) and corresponding unit cells
Abstract:
Four-way symmetric translational tiles are typically observed in crystals with a fourfold rotational symmetry. These tiles can form various types of crystal lattices, depending on the arrangement of the tiles and the choice of unit cell. A Penrose collage may possess (so defined) five-fold rotational symmetry (on a specific point) and reflection symmetry, but not translational symmetry. Given the widespread acceptance of (so defined) five-fold rotational symmetry as a distinguishing feature of Penrose tiles, it appears no one believe that four-way symmetric Penrose tiles can be easily made. The most intriguing discovery is that Penrose tile has an infinite capacity for self-extension in translation, and with all six different inner-structure decagons coexisted.
The unlimited unit cell can be easily extracted from the tiling (crystal) that by coupling scheme of different Pentangular Penrose tiles ,that may be very useful to image the structures of new quasi crystals.
Audience Take-Away:
- The definition of crystal
- Build an Imagination of quasicrystal
- Solid state physics
- It helps to draw an infinite large Penrose tiles, and perceives what it looks like at infinity
- You may make an unlimited combination with basic circular and Pentagonal shape Kung’s clusters.
- It will make a lot of money, if printed in 3mX3m, with million diamonds, and all six different Decagons coexisted. At least one million with my signature.
