Skip to main content

Escher-Like Patterns from Pentagonal Tilings

  • Chapter
M.C. Escher’s Legacy

Abstract

My first acquaintance with tiling pentagons was from Martin Gardner’s “Mathematical Games” columns in Scientific American magazine, in July and in December 1975. Although every triangle and every quadrilateral can tile the plane (that is, fill the plane with congruent copies, without gaps or overlaps), only certain types of pentagons can tile the plane. Until Gardner’s article, it was believed that all such types were known; there were eight different types.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Martin Gardner July 1975. “On tessellating the plane with convex polygon tiles.” Mathematical Games, Scientific American, pp. 112–117.

    Google Scholar 

  2. Martin Gardner 1988. “Tiling with Convex Polygons.” Time Travel and other Mathematical Bewilderments. W.H. Freeman & Co. pp. 174–175. [This reproduces the 1975 column of [1] and gives updates on the aftermath of the column.]

    Google Scholar 

  3. Daniel Huson and Olaf Delgado Friedrichs 1992–95. RepTiles, computer software to produce k-isohedral tilings.

    Google Scholar 

  4. Ivars Peterson 1990. “Paving the Plane.” Islands of Truth. W.H. Freeman & Co. pp. 83–86.

    Google Scholar 

  5. Doris Schattschneider 1981. “In Praise of Amateurs.” The Mathematical Gardner, edited by David A. Klarner. Wadsworth International, pp. 140–166.

    Chapter  Google Scholar 

  6. Doris Schattschneider. Jan. 1978. “Tiling the Plane with Congruent Pentagons.” Mathematics Magazine, pp. 29–44.

    Google Scholar 

  7. Doris Schattschneider Nov. 1985. “A New Pentagon Tiler.” Mathematics Magazine, cover and News and Notes.

    Google Scholar 

  8. Doris Schattschneider and Marjorie Rice. Dec. 1980. “The Incredible Pentagonal Versatile.” Mathematics Teaching pp. 52–53.

    Google Scholar 

  9. Doris Schattschneider 1990. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher. New York: W.H. Freeman & Co.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rice, M. (2003). Escher-Like Patterns from Pentagonal Tilings. In: Schattschneider, D., Emmer, M. (eds) M.C. Escher’s Legacy. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28849-X_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-28849-X_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20100-7

  • Online ISBN: 978-3-540-28849-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics