Octamatch - 8 sided edge-matching

Octamatch

This edge matching puzzle was conceived by Zdravko Zivkovic and is published and sold by Kadon Enterprises under the name Doris.
It was named the Winner in the Puzzle category in the GAMES (magazine) 100 for the year 2009.
Zdravko has also created a delightful animation, available on Youtube.

The puzzle consists of 24 octagonal pieces, with segments colored using all combinations of three colors.

Pieces can be placed with two orientations.

If the edges of the interior square are horizontal/vertical, it is a "square" placement.

Rotated 45°, it is a "diamond" placement.

A solution is reached when all pieces are placed, and wherever two of them meet, the colors match, as shown here:

The puzzle has millions upon millions of solutions, with the numbers varying greatly from one configuration to the next.

In general, squares are much easier to fit together than diamonds because only one color need be matched per side instead of two. For example, the 4x6 pattern with four columns of diamonds and two columns of squares in the center has just under ten thousand solutions. (9951 to be exact). The reverse pattern, four columns of squares and two of diamonds has 63,275,298!

On these pages we explore just a few of the possibilities, classifying them by a pattern of diamonds and squares and the placement of the three one-color (solid) pieces.

See below for results for quite a few of them.

You can explore the set and its possibilities with this ONLINE VERSION.

Symmetric (and Near-Symmetric) Solutions

Because there are 3 colors, perfect symmetry is not achievable on the standard rectangular figures, but it's possible to get close. The best so far is just two pairs of piece segments (4/96) mismatched. If we allow a bit more freedom in designing the figure, including a piece connected to others by only one edge, then perfect symmetry can be realized.

	Figures with 100% symmetry

Solids in the middle 93% Symmetry	Solids along one edge 90% Symmetry	Diagonal symmetry

On a 5x5 grid (center space omitted), there are 182 possible placements of the three one-color pieces, disregarding those which are symmetric to one of those 182. On a 4x6 grid, there are 319 possible placements of the solids, and on a 3x8 grid, 382.

Where the pattern is asymmetric with regard to the solids, different rotations of the pattern are explored.

Click on a figure to see solutions with its pattern.