Cell Shifts for Polykings

Introduction

Two figures can be tiled with copies of the same polyking. The figures differ in only one cell. How near can the unmatched cells lie?

Over all such pairs of figures, a minimal vector from one unmatched cell to the other is called a minimal shift vector. Here I show minimal shift vectors for polykings up to order 5.

I do not consider polykings that are polyominoes or slanted polyominoes. See Cell Shifts for Polyominoes.

If you find a shorter shift for a solved polyking or solve any of the unsolved polykings, please let me know.

Triking

(1, 0)

Tetrakings

	(1, 1)
	(1, 1)
	(1, 1)
	—
	(6, 0)
	(1, 1)
	(1, 1)
	(1, 1)
	—
	(6, 6)
	(3, 3)
	—

Pentakings

	(1, 0)
	(1, 0)
	(1, 1)
	(1, 0)
	(3, 0)
	(1, 1)
	(3, 3)
	(1, 1)
	(1, 1)
	(1, 0)
	(1, 0)
	(3, 0)
	(3, 3)
	(1, 0)
	(1, 0)
	(1, 1)
	(3, 3)
	(1, 0)
	(1, 0)
	(1, 1)
	(3, 3)
	(1, 0)
	(1, 0)
	(1, 0)
	(1, 0)
	(1, 0)
	(1, 1)
	—
	(6, 0)
	(1, 1)
	(1, 1)
	(1, 0)
	(1, 1)
	(1, 0)
	(1, 0)
	(3, 3)
	(3, 3)
	(3, 0)
	(1, 0)
	(3, 0)
	(3, 0)
	(1, 1)
	(1, 1)
	(1, 1)
	(1, 1)
	(1, 0)
	(3, 0)
	(1, 1)
	(1, 0)
	(1, 0)
	(1, 0)
	(1, 1)
	—
	(1, 0)
	(1, 1)
	(1, 1)
	(5, 0)
	(1, 0)
	(1, 0)
	(1, 1)
	(1, 0)
	(1, 1)
	(12, 0)
	(6, 6)
	(1, 0)
	(1, 1)
	(3, 0)
	(1, 0)
	(1, 0)
	(1, 1)

Last revised 2024-05-20.

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Col. George Sicherman [ HOME | MAIL ]