Pentapenny Compatibility

Introduction

A pentapenny is a plane figure formed by joining five equal discs tangentially. Two pentapennies are considered the same if there is a topological homeomorphism of the plane that converts one to the other. By this criterion there are 13 different pentapennies:

Two pentapennies are compatible if there is a polypenny that can be completely tiled by either. Here I show minimal known compatibility figures for pairs of pentapennies.

If you find a smaller solution or solve any of the unsolved cases, please let me know.

5A—5D5A—5I5A—5K5A—5M
5A—5O5A—5P5A—5Q5A—5R
5A—5T5A—5V5A—5X5A—5Y
5D—5I5D—5K5D—5M5D—5O
5D—5P5D—5Q5D—5R5D—5T
5D—5V5D—5X5D—5Y5I—5K
5I—5M5I—5O5I—5P5I—5Q
5I—5R5I—5T5I—5V5I—5X
5I—5Y5K—5M5K—5O5K—5P
5K—5Q5K—5R5K—5T5K—5V
5K—5X5K—5Y5M—5O5M—5P
5M—5Q5M—5R5M—5T5M—5V
5M—5X5M—5Y5O—5P5O—5Q
5O—5R5O—5T5O—5V5O—5X
5O—5Y5P—5Q5P—5R5P—5T
5P—5V5P—5X5P—5Y5Q—5R
5Q—5T5Q—5V5Q—5X5Q—5Y
5R—5T5R—5V5R—5X5R—5Y
5T—5V5T—5X5T—5Y5V—5X
5V—5Y5X—5Y  

Last revised 2017-08-17.


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Col. George Sicherman [ HOME | MAIL ]