Got to wondering about the Nh8: what is its meaning in life. Well, it protects its brother on g6, but White already has a bishop and queen doing that. But supposed they have to do something else?

Also, consider the 1...Rg4 defense. In the diagram that is answered by 2.Nf4#, possible because the Bf6 now covers h4. However, White can't maintain that without conceding something else. What to do?

Nope. There is only one key move and one mate for each possible black response. If you think you've ever found an alternate solution, you can hover your mouse over "Options" (don't click!), wait for the flyout menu, and then click "Another Solution".

phonybenoni hit the nail on the head. I initially dismissed the solution because I didn't see the response to 1...Rxg6. I came back to it because, well...it has to be right. No other pieces can move and no other destination provides sufficient coverage. Very elegant construction.

(P.S. phonybenoni, your commenting style has developed an elegance of its own. Your thoughtful notes are much appreciated. Makes up for the good professor donnaclara's absence.)

That wss awesome with so many variants

Strangely, it was the pawn on d4 that provided me with the clue.Why is it there? Because it prevents 1...Be5, which forestalls the mate with R on h2. The question then was: why should the black bishop move it all. That made me realise it was going to be a zugzwang situation, and led me to look for any move by Black for which White did not already had a mating response. One such move is 1...Rxf5.  

Mmm, yes, you're right.