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Minimal regular polygons serving as universal covers in R 2

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Abstract

A universal cover is a set K with the property that each set of unit diameter is a subset of a congruent copy of K. It is shown that the smallest regular n-gon, for fixed n ≥ 4, which serves as an universal cover in R 2 is the smallest regular n-gon covering a Reuleaux triangle of unit width.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, CA, USA

    Don Chakerian

  2. Department of Mathematics, Santa Clara University, 95053, Santa Clara, CA, USA

    Dave Logothetti

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  1. Don Chakerian
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  2. Dave Logothetti
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Chakerian, D., Logothetti, D. Minimal regular polygons serving as universal covers in R 2 . Geom Dedicata 26, 281–297 (1988). https://doi.org/10.1007/BF00183020

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  • DOI: https://doi.org/10.1007/BF00183020

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