There was no such pharaoh of the 12th dynasty. I'd guess you mean Amenemhat_II. And the style of those pharaohs who were in the 12th does indeed match with the Great Sphinx. See also Senwosret III as a Sphinx.
Here's one of the 18th dynasty pharaonic sphinxes:
One of his successors, Thutmosis IV, had the Dream Stele erected after clearing the Sphinx enclosure of sand. The problem with the pharaohs of the 18th (and the 4th, for that matter) was their lack of the jutting chin seen on the Great Sphinx itself -- more likely black African.
Spelling spelling - sorry again. Senwosret III has ‘sad’ eyes and wrong headdress, Thutmose III has rounded cheeks and wrong headdress so not them either.