A324494 Coordination sequence for Tübingen triangle tiling.

1, 10, 10, 20, 50, 30

Offset: 0

Author

N. J. A. Sloane, Mar 12 2019

Keywords

• nonn
• more

Comments

Also known as the Tubingen or Tuebingen tiling. - N. J. A. Sloane, Jul 26 2019

The base point is taken to be the central point in the portion of the tiling shown in Baake et al. J. Phys. A (1997)'s Fig. 2 (left).

Note that the points at distance 2 from the base point, taken in counterclockwise order starting at the x-axis, have degrees 8, 7, 6, 8, 7, 6, 7, 8, 6, 7, so the figure does not have cyclic 5-fold symmetry (even though the initial terms are multiples of 5). There is mirror symmetry about the x-axis.

For another illustration of the central portion of the tiling, see Fig. 3 of the Baake 1997/2006 paper. - N. J. A. Sloane, Jul 26 2019

References

• Baake, Michael. "Solution of the coincidence problem in dimensions d <= 4," in R. J. Moody, ed., The Mathematics of Long-Range Aperiodic Order, pp. 9-44, Kluwer, 1997 (First version)

Links

• M. Baake, J. Hermisson, P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See Fig. 2 (left).
• Michael Baake, Solution of the coincidence problem in dimensions d≤4, arXiv:math/0605222 [math.MG], 2006. (Expanded version)
• N. J. A. Sloane, Illustration of initial terms. [Annotated version of Fig. 2 (left) of Baake et al. 1997.]
• Index entries for coordination sequences of aperiodic tilings

Crossrefs

Cf. A303981.