Representing Tiling and Packing Solutions

[Edward Vogel]

I have been long interested in how one might find all of the 240 unique solutions to the SOMA cube puzzle since receiving one for Christmas in 1968. If one were to find all of the solutions (many of them are "similar" and there is an interesting variety "similar" to boot) . . how best to represent them. Conway and Guy came up with the SOMAP:
http://www.fam-bundgaard.dk/SOMA/NEWS/N030518.HTM

Which is a very beautiful structure but a bit hard to decode into solutions. A friend of mine did some work decoding it:
http://artisticapproach2math.blogspot.com/2016/05/somap-tips-tricks-and-other-stuff.html

Perhaps a tree graph? Not nearly as elegant as the SOMAP:
http://artisticapproach2math.blogspot.com/2016/09/graphs-and-solutions-representation.html

Anyone have any thoughts?

 

[mmwave]

Thank you for your interest in finding all 240 unique solutions to the SOMA cube puzzle. It is certainly a fascinating challenge and one that has intrigued many since its creation in 1936.

In terms of representing the solutions, there are a few different options that you could consider. As you mentioned, the SOMAP created by Conway and Guy is a beautiful structure, but may be difficult for some to decode. However, it does provide a visual representation of the solutions that may be helpful for some individuals.

Another option could be to create a tree graph, as you suggested. This would allow for a more organized and systematic representation of the solutions. However, as you mentioned, it may not be as elegant as the SOMAP.

One potential solution could be to combine the two approaches. You could create a tree graph that is based on the SOMAP structure. This would allow for a more organized representation while still incorporating the beauty of the SOMAP.

Ultimately, the best way to represent the solutions may depend on the purpose of the representation. If it is purely for personal use, then the approach that works best for you may be the most effective. However, if the goal is to share the solutions with others, it may be beneficial to consider different options and choose one that is more easily understandable for a wider audience.

I hope this helps and I wish you the best of luck in your quest to find all 240 unique solutions!