A gargoyle constable in the Ankh-Morpork City Watch. One of two representatives of his species in the Watch, along with Constable Downspout. They are brilliant on stake-outs as they are practically world champions at staying in the same place and watching for as long as it takes. They are paid in pigeons. Well, what the hell else would a sentient statue want? Money'd be no good!
"Pediment" seems to be a common gargoyle name, as an "Old Pediment" who is apparently a different gargoyle appears in The World Of Poo.