Pentimoes

I have recently discovered that online manufacturers and rapid prototyping services have become very competitive both in terms of their prices and the quality of their product. In the past, these services could only make products from brittle styrenes and acetates, and for outrageous prices. They now offer a broad selection of materials including wood and stainless steel, and the overall cost is cheaper now than ever.

The 1/1/1/1/1 Pentimo

Amongst my game ideas, I have spent some time working on pentagonal dominoes. In the past I have tried to find some pentagonal tiles or blocks that I could mark on to experiment with rules and scoring, but to no avail. I am now committed to making a set of these 'Pentimoes' in a fairly affordable and durable material.

I modeled a small series of them up in AutoCAD, and uploaded them to a stereo-lithography service to get a price quote: it was still too rich for my blood. I then looked into other methods, and found I could have them laser-cut from wood at a fraction of the cost!

I haven't finished the cut-file and spec'ing the design, but based on the pricing of the test file I uploaded, I expect it to cost about $140 for the set.  While it is an outrageous price for a regular set of dominoes, these are not regular, and considering I have been unable to find even something with a pentagonal cross section I could cut into tiles, let alone actual pentagonal tiles, This seems like a fair price.

Before I submitted a design, I needed to choose what units were going to be on the pentimoes, their distribution and arrangement.  The original pentimo sketch had random scratching on each face, while later sketches used conventional numbers. I briefly considered using some collection of wing-dings or shapes, but ultimately decided to go with the domino standard: pips.

Domino tradition also dictated that there would  be one pentimo for every possible combination of pips in a set. Because pentimo have 5 faces, the number of pentimo for even a small range of pips was huge. Luckily because off their radial nature, a 1/1/1/1/2 pentimo is the same as a 2/1/1/1/1 pentimo, its just a matter of orientation. Clock-wise or counter-clockwise does matter though: 2/3/1/1/1 is the same as 1/1/1/2/3, but not the same as 3/2/1/1/1.  With all that in mind, I settled on making a set of pentimoes with 1, 2, or 3 pips per face. That gives 243 total combinations, but ruling out radial redundancies, that leaves 51 unique combinations. Considering a set of double 6's has 21 dominoes, 51 seemed like a fine number.  Besides, fitting more than 3 pips along a face would have been daunting.

The CAD file with pip combinations.

That information has now been graphically incorporated into the cad drawing, and just needs to be converted into a format the laser cutter can work with.

I spent a lot of time trying to optimize the fill pattern while maximizing shared cut lines to reduce cut-time. Ultimately, because cutting costs are much higher than material costs, wasted material is less sinful than excessive cutting.

The only thing left to do is get a set shipped to me, and set to work on games and rules. Luckily, dominoes are like playing cards: There is no official game, let alone a single set of rules for any given game. I can comfortably create as many rule variants as I want, without feeling the need to pick a winner!