Tiling a Chamfered Rectangle with Three Pentaboloes

Introduction

A pentabolo or pentatan is a plane figure formed by joining five equal isosceles right triangles at their legs or hypotenuses. Here are the 30 pentaboloes:

A chamfered rectangle is a rectangular polyabolo with its corner cells clipped diagonally. To prevent cuts from meeting, I require the dimensions of the rectangle to be 3 or greater.

Here are chamfered rectangles tiled with copies of three different pentaboloes. There are 4,060 sets of three pentaboloes, too many to show here. Instead I show the minimal known tilings that have at least 150 tiles.

See also

  • Tiling a Chamfered Rectangle with Two Pentaboloes
  • Tiling a Chamfered Rectangle with Two Tetraboloes
  • Tiling a Chamfered Rectangle with a Polyabolo
  • 150 Tiles

    154 Tiles

    156 Tiles

    172 Tiles

    184 Tiles

    204 Tiles

    244 Tiles

    254 Tiles

    268 Tiles

    Last revised 2024-04-13.


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    Col. George Sicherman [ HOME | MAIL ]