New answers tagged tiling
4
votes
Accepted
For what $n$ do there exist non-periodic tilings with rotational symmetry of order $n$?
Jarkko Kari and Markus Rissanen construct such (even a substitutive one), called Sub Rosa, for even $n$ in [1]. ArXiv is https://arxiv.org/abs/1512.01402
The second-named author is Markus Rissanen, ...
- 6,652
1
vote
Tiling with ten-fold symmetry and (unoriented) Penrose tiles?
The division of a pentagon into triangular pieces described here can be used to generate a tenfold quasilattice. At each node generated by any iteration additional edges are rendered in subsequent ...
- 2,370
22
votes
Accepted
Can you see through a cannonball packing?
Yes. View the FCC packing as a series of stacked square packings, with spheres of unit radii centered at the points $(2a,2b,2\sqrt{2}c)$ and $(2a+1,2b+1,(2c+1)\sqrt{2})$ for all $a,b,c,\in\mathbb Z$:
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- 3,068
6
votes
Tiling with ten-fold symmetry and (unoriented) Penrose tiles?
We can start with a floret that looks like this:
then follow the following substitution rules (repeatedly) :
this yields a tiling, part of which is shown below.
Some things to note about this ...
- 263
10
votes
Accepted
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