Leg support for travertine countertop

[BuildingNovice]

We are looking to have a 30mm block of travertine embedded into a corner in the bathroom to act as counter for sink.

2 sides of block can be embedded a few cm into tiles/stud joists for support, but the opposite corner will need support. It would look best if we got another travertine block to act as a leg - question is how best to secure this block to floor and the horizontal block?

I'll be grateful for any pointers.

 

[TicklyT]

My immediate thought is to drill both ends of the 'leg', the bottom of the counter and the floor for some steel dowel pins.

That's more or less the way the lintels on Stonehenge were secured, so it should work.