Cell Shifts for Polyiamonds

Introduction

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 polyiamonds up to order 7. Values in red are unproven. The nontrivial proven values are by Mike Reid, using Tile Homotopy Theory. For polyiamonds of order 8, see Cell Shifts for Octiamonds.

If you can solve any of the unsolved cases, please let me know.

Moniamond

1

Diamond

√3

Triamond

1

Tetriamonds

	2√3
	√3
	—

Pentiamonds

	1
	1
	1
	1

Hexiamonds

	3√3
	√3
	—
	3√3
	√3
	√3
	3√3
	√3
	3√3
	—
	√3
	—

Heptiamonds

	1
	1
	1
	1
	1
	1
	1
	6√3
	1
	1
	1
	2
	—
	1
	1
	1
	1
	1
	1
	1
	1
	—
	1
	√3

Last revised 2012-01-14.