Throwing Five 6s asked if five ordinary dice were thrown until each individual die had thrown its maximum value (6) at least once, what was the expected number of throws to complete the set. Once a given die had reached its goal, it was set aside so as to keep track of the remaining dice.

Suppose we do that with tosses of coins or of dice of all the shapes of Platonic solids (4- 6- 8- 12- and 20-sided dice), considering heads to be the highest side of a coin.

Find, for 1 through 20 dice of each of these numbers of sides (2, 4, 6, 8, 12, 20) the expected number of tosses to get each die (or coin) to have shown the highest of its values, to 10 significant digits (no need to show the rational number as in the previous puzzle).