Omnimaga
General Discussion => Other Discussions => Math and Science => Topic started by: ruler501 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.
-
What do you mean by "Unique Representation of Cube Configurations"?
-
My guess: http://en.wikipedia.org/wiki/Polycube
Good luck with 6 :P
-
According to wikipedia there are 112 unique combinations for 6. Have fun.