Catalogue of Polymings

A polyming is a figure made of equal equilateral triangles on the polyiamond grid, joined along edges or at vertices. It is a generalization of a polyiamond. (In the Online Encyclopedia of Integer Sequences, David Bevan calls polymings polyglasses.)

Here I show all the polymings with from 1 to 4 cells.

Two-sided polymings are identified under reflection as well as rotation. One-sided polymings are distinguished under reflection. That is, if a polyming and its mirror image are distinct, both are counted.

Enumeration

Order	Two-Sided	One-Sided
1	1	1
2	3	3
3	11	16
4	75	129
5	528	1 009
6	4 584	8 997
7	40 609	80 816
8	373 981	746 483
9	3 493 723	6 983 847
10	33 079 702	66 146 105

The figures below show two-sided polymings.

Monoming

Dimings

Trimings

Tetramings

Last revised 2021-01-03.

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Col. George Sicherman [ HOME | MAIL ]