Is there a standard way to number the faces of a 20-sided die?
I assume that we are speaking about a D20 that makes some attempt to roll fairly, such as the ones used in D&amp;D. This is different from the aptly named "spindown" D20 which is numbered in a simple spiral.

Why do opposing faces add up to 21?

According to Everything2.com's article on D20, opposing sides add up to 21 so that the numbers most distant from each other to appear on opposite sides of the die.

Ok, now we have 10 pairs of 21. How do we arrange them?

If you are engraving the numbers, you'll have to carve out more material for some numbers than for others. The more you dig out, the lighter that side becomes.

Everything2 advises that we arrange these pairs in a way that heavy sides are next to light sides, but they provide no actual arrangement. In fact, I cannot find any actual mathematics behind what the best possible arrangement actually is. After a substantial amount of searching, I have concluded that the "standard" arrangement we know today probably originated from D&amp;D, but I can't back this up.

Speaking of standard arrangement, here is the actual answer to your question.



Image from DiceCollector.com