### Author Topic: Unique Representation of Cube Configurations  (Read 1898 times)

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#### ruler501

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##### Unique Representation of Cube Configurations
« on: November 30, 2012, 11:13:54 pm »
In my engineering class our teacher gave us a challenge to draw a sketch of every unique combination of 3,4,5, and 6 cubes. I spent about 30 minutes on that before I realized that I was making lots of duplicates. I wanted to find a way to tell if one would be unique without having to actually make it. I'm not good at rotating it in my head so I wanted something like a formula for uniqueness. I was thinking maybe something like the polynomials, sets, and numbers used to represent knots would work, but I haven't been able to figure out how to do that.

The approaches I have tried are as follows:
Have a set of numbers that just contains how many cubes it touches
Have a set of ordered pairs/trios/etc that are at junctions that say how far it goes in each direction
Have a sets of ordered pairs like above just group them with a number that says what the shortest straight line distance between the junctions are.

I saw that all of these failed. How else could I do this and would a representation allow me to generate all possible cubes without brute forcing it.
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#### AngelFish

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##### Re: Unique Representation of Cube Configurations
« Reply #1 on: November 30, 2012, 11:22:51 pm »
What do you mean by "Unique Representation of Cube Configurations"?
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#### phenomist

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##### Re: Unique Representation of Cube Configurations
« Reply #2 on: December 01, 2012, 12:14:06 am »
My guess: http://en.wikipedia.org/wiki/Polycube

Good luck with 6
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#### willrandship

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##### Re: Unique Representation of Cube Configurations
« Reply #3 on: December 01, 2012, 04:47:02 am »
According to wikipedia there are 112 unique combinations for 6. Have fun.
« Last Edit: December 01, 2012, 04:47:10 am by willrandship »