JJ, you said the (block?) was for the after shave, do you rub it over your face sort of like a exfoliate?
Funny you asked that. I just got finished reading the wiki article on alum.
Alum, in this case potassium alum, has coagulant and anti-microbial properties. It also tightens the skin.
Do you remember the old cartoons when Tom would get alum in his mouth and his mouth would shrink too small to eat Jerry?
These qualities are why it is used as after shave. Get the stone wet and rub it on. It stings a little at first, at least where the nicks are, but then feels soothing.
Cultures like ones in Thailand use these stones as deodorant since it retards the growth of bacteria.