No, no.... Using that original formula of "720 (integer degrees from -360 to 360) times 3 (x, y and z rotations) times 3 (number of body parts) = 6,480 combinations" The problem isn't one of dimensions, it is in calculating the permutations. Take a single 6-sided die. One die has 6 possible positions. Two dice have 36 possible combinations. The answer isn't 6x2; it is 6^2 In this case we have, say, 360 possibilities on three axis on at least three joints (shoulder, elbow, wrist). (360^3)^3 or 360^9 equals 1.016 EE 23 (1 followed by 23 zeroes). If you added finger joints it might be, say, 360^12 and we get up to 4.7 EE 30 (sorry to change notation there; also known as 4.7 x 10^30, or maybe just 4,700,000,000,000,000,000,000,000,000,000 ). That's what Ajax is saying. Number of dimensions doesn't matter per se. It's the difference between multiplying and raising to a power! So be proud -- you've found a way to filter through a much, much greater number of choices than you thought!