About the Tricolor Stomachion monograph


The story of the Tricolor Stomachion goes back 2200 years, traced through an ancient parchment, the Archimedes Palimpsest. Kadon started making copies of the puzzle in 2003, in solid colors. In 2011, Kate decided to jazz it up a bit by using three colors per set, such that no two of the same color touched on more than one point and that all three colors contained the same area.

Also in 2003, Bill Cutler was the first to prove that Archimedes' Square, the Stomachion, had exactly 536 solutions. When the puzzle acquired three colors, that number doubled, to 1072, because two congruent triangles that originally were the same color now were differently colored. Here is their chart:




In 2017, Joe Marasco became curious about the way the three colors occurred in all those solutions, and he set in motion a major research project to analyze and group the solutions by how many pieces of the same color were joined and how many color regions they produced. A six-month search involved coloring in all 1072 solutions (thank you, Alex Streif, for this astounding feat), cataloguing them by type, and organizing them into columns and rows for cross-reference (thank you, Dick Jones, for dictating from Maryland all the numbers by phone to Kate in Florida to transcribe).

Joe, in the meantime, was drafting a scholarly article about this project and converting the statistics that Alex and Kate had produced into a Concordance that thoroughly documented and charted all the solutions by frequency and type of color regions—how many of each kind of color adjacency occurred? Which ones were the most numerous? Which ones were the rarest? Here is the statistical line-up, the "matrix map", of all the different types of solutions:

The Monograph tells this story in spell-binding form and shows all the results. It makes a fine companion to the puzzle itself and is available as a separate publication for purchase. The Monograph by itself is $10.72. Accompanying the purchase of the Archimedes' Square, the Monograph is only $5.00.

Add to your order, Monograph alone, $10.72
Add to your order, Monograph with Archimedes' Square, $47.00



This historical adventure inspired Kate to write this little poem for Kadon's Renaissance Festival catalog and to present it at the Bridges 2017 poetry reading session, accompanied by on-screen illustrations:

Stomachion, the Quest

What marvel of antiquity be this,
This fabled square of 14 parts comprised?
Behold the oldest puzzle ever told,
Our heritage of mind, millennia old.

Now scholars scrambled to decode, with zest,
Archimedes’ much-prized Palimpsest,
A scroll long lost, inscribed by ancient hands,
A rarest find from Greek and Latin lands.

Then three-fold color sought to split the tiles
That matchless equal areas beguile.
Five hundred thirty-six assemblies wait
Concordances and catalogs to mate

As solvers brave and eager in their sport
The joined and varied regions rightly sort.
That tale is told with elegance and charm
As Joe and team each gave a leg and arm.

— Kate Jones, 2017



Then, in 2018, Joe Marasco created a fascinating video documentary on the Tricolor Stomachion you can watch on YouTube, about the historical origin and tricolor development of Archimedes' Square.


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