Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-13T03:35:33.100Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes: 61.25 Prescribed numbers of tiles and tilings

Published online by Cambridge University Press:  22 September 2016

Heiko Harborth
Heiko Harborth*
Affiliation:
Technische Universität Braunschweig, D33 Braunschweig, West Germany
Get access Rights & Permissions [Opens in a new window]

Extract

In their recent article [1] B. Grünbaum and G. C. Shephard asked whether, for every pair of natural numbers k, r, there exist sets of k tiles that admit precisely r distinct tilings of the plane. (Two tilings are said to be distinct if they cannot be brought into coincidence by a rigid motion, and it is to be understood that in the tilings each distinct tile must occur at least once.) They gave examples for k = 1, r = 1, 2 and for k = 2, r = 1, and referred in a footnote to a later discovery of a solution for k = 1, r = 3.

Type
Research Article
Information
The Mathematical Gazette , Volume 61 , Issue 418 , December 1977 , pp. 296 - 299
Copyright
Copyright © Mathematical Association 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Grünbaum, B. and Shephard, G. C., Patch-determined tilings, Mathl Gaz. 61, 31–38 (No. 415, March 1977).Google Scholar