Answer: A Grotesque

Although the term “gargoyle” is commonly used to refer to any sort of statue-like ornamentation that decorates the corners and pinnacles of buildings, traditionally, a gargoyle is a functional piece of ornamentation that directs water away from a building—the word is French for throat (“gargouille”) and is also the source of the modern word “gargle”.

Gargoyles were commonly designed as screaming creatures, demons, or animals precisely because their open mouths were practical termination points for the gutters directing water off the roof.

A statue that appears to be a gargoyle but only serves a decorative function is known as a grotesque—traditionally, the same styling as a gargoyle, but sans the practical use of redirecting water.