Catalogue of Polycrowns

A crown is an equilateral pentagon made by altering the positions of two adjacent sides of a regular pentagon.

A polycrown is a plane figure formed by joining crowns edge to edge. Irmi Beyer introduced the terms crown and polycrown in 2025 in the Facebook group Mathematical Tiling and Tessellation. The crown is also known by names like dented pentagon, collapsed pentagon, and concave pentagon.

Livio Zucca analyzed crown tilings in 2003. You may see his results here at his site Remembrance of Software Past.

Yoshiaki Araki (荒木義明) has determined the convex spectrum of the crown pentagon. You may see his results on this page of Erich Friedman's Math Magic.

Here I show all polycrowns with 1, 2, or 3 cells. Irmi Beyer enumerated those with 1 and 2 cells.

See also

  • Galvagni Figures for Polycrowns
  • Baiocchi Figures for Polycrowns
  • Enumeration

    Two-sided polycrowns identify mirror images. One-sided polycrowns distinguish mirror images. This catalogue shows two-sided polycrowns.

    CellsTwo-SidedOne-Sided
    111
    2712
    362119
    48581 694

    Rick Mabry enumerated the tetracrowns, subject to review.

    Monocrown

    Dicrowns

    Tricrowns

    Last revised 2025-07-25.


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    Col. George Sicherman [ HOME | MAIL ]