Pete - your facets are a tpe of decoration called sliced cut, and the construction is a drawn shank or drawn stem i.e. the stem is created by drawing glass away from that of the bowl, making a two piece glass (the other 'piece' being the foot). Not a rummer though, and I might suggest this is a port or sherry (traditionally, port glasses were a little smaller than sherry glasses) - and Anne's comments about width of foot are correct, in general, although there are always exceptions.
Unfortunately, you don't comment about the foot at all - if there is a polished pontil scar they have some quality - if not and you have a 'gadget mark' (unlikely I think) then less quality. Date wise they might be anywhere from 1860 to 1900 - and wear, if any, might help you here. If they 'ring' well, then they should contain lead, but not sure about your comments regarding resonance.
There are such poionters as looking for the shears mark on the rim - looking for stones in the glass - and the colour of the glass might also help to date this piece, but pound to a penny it's Victorian.
