On the arrangement of digits on a dice

Question

In a cubic dice, the sum of the numbers on 2 opposite faces is 7, why are numbers arranged in such a way? Would the result of throwing a dice (1 or more times) still yield a random number if the numbers were arranged differently? Thanks.

Answer 1

A fair die is equivalent to a random integer generator on the set $\{1, 2, 3, 4, 5, 6\}$. Of course, the order of the integers doesn't matter, so neither do the arrangement of the numbers on the die.

But to answer your question about why this arrangement, according to http://en.wikipedia.org/wiki/Dice, this is presumably so the 1, 2, and 3 faces of the die share a vertex, which is aesthetically pleasing.