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 Post subject: Soma Dice Cube and Building Polycube Puzzles
PostPosted: Mon Jan 13, 2014 2:54 pm 
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Joined: Sun Nov 23, 2008 2:18 am
It is a well-known fact that the Soma Cube has 240 solutions, but I was wondering how things change if the unit cubes were replaced by six-sided dice such that each piece has all of its dice orientated in the same direction and requiring that a solution only counts if each side of the cube has all the same number.

A single die can be orientated in 24 ways, but symmetry of the bent tricube and the tetracubes should render some orientations indistinguishable in the constructed pieces.

So my questions are:
1. For each piece of the Soma cube, how many visually distinct ways can the piece be constructed from dice with the restriction that the dice all be oriented in the same direction?
2. How many distinct sets of Dice Soma pieces are there?
3. How many solutions with each side having all the same number exist for each set of pieces?

Also, since the Soma cube appears to be one of the few polycube puzzles(Assembly/Packing puzzles where you are given a set of polycubes and must construct a box of given size or a given shape) that is readily available in a mass produced form, can anyone suggest a good method for constructing my own polycubes. Best idea I have come up with is buying six sided dice in bulk(I have found some on Amazon for around 15USD for a 100) and gluing them together, which while cheap for material costs could get quite labor intensive if I way, wanted to build a complete set of flat hexacubes or multiple complete sets of tetracubes.

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 Post subject: Re: Soma Dice Cube and Building Polycube Puzzles
PostPosted: Tue Jan 14, 2014 3:12 am 
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Joined: Thu Apr 19, 2012 6:33 am
Location: Belgium
I made a lot of puzzles lately with wooden Cuisenaire rods, very easy, they come in different lenghts from 1 to 10 centimeter, all I have to do is glue them together. You can buy new ones or vintage, the new ones are more precise, vintage is cheaper, only problem is that the rods are a bit small.

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 Post subject: Re: Soma Dice Cube and Building Polycube Puzzles
PostPosted: Sun Jan 26, 2014 6:58 pm 
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Joined: Sun Nov 23, 2008 2:18 am
Ordered one of the small 155 piece sets of Cuisenaire rods, and while I will agree they are quite small(you don't realize just how small cubic centimeters are until you roll a 1cm cube between your fingers), but they probably offer about the best balance of low cost and low labor I am going to find, and the small size might actually come in handy with building larger polycube sets. Also bought a 100 pack of d6's to build a dice Soma Cube and a dice Bedlam Cube.

Any suggestions on how best to glue the cuisenaire rods or dice together? Also, can anyone answer the following question:
Are their any possible set of Soma/Bedlam cube pieces built from aligned dice that produce no solution where each side of the assembled cube has all the same number?

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I pledge allegiance to the whole of humanity, and to the world in which we live: one people under the heavens, indivisible, with Liberty and Equality for all.

My Shapeways Shop


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