Polyiamonds, polyhexes and other polyforms

This site was initially intended as a mean of sharing the dodecahexes that can be tiled with hexiamonds. The hexiamonds themselves are geometrical shapes formed of exactly six equilateral triangles. There exist 12 hexiamonds, if we do not consider rotated and mirrored shapes as different. They cover a total of 72 equilateral triangles. As for the dodecahexes, these consist of twelve hexagons. However, once this problem was extensively solved by George Sicherman, I started publishing various other ideas and results about polyforms, especially polyiamonds and polyhexes. My own partial results for the dodecahexes problem can still be seen here.

Unless explicitly stated, all problems presented here use exactly once each piece of a given set of polyforms, i. e. I don't analyse problems with repeating or missing pieces.

Mathematical Problems

Artistic Creations

JavaScript solvers

You can use my JavaScript solvers for easy puzzles. The user interface is a bit confusing: click on a cell to fill or unfill it. Click on the right-most coloured cell to solve the puzzle. Use the middle yellow cell to visualize a particular solution. To discover the use of the other colours cells, move your mouse over them (works only on a computer, not a smartphone).

Triangle based puzzles

Square based puzzles

A demonstration of the order in which Algorithm X places the pieces in an octiamond shape. This algorithm chooses always the place where the least number of pieces can be placed. This makes it faster than choosing places in a predefined order (for instance filling line after line top to bottom).


Developed by Todor Tchervenkov: tchervenkov@gmail.com