Dreadful older phony that's more than two-faced (10)
I believe the answer is:
polyhedron
'that's more than two-faced' is the definition.
(a polyhedron is a solid with many faces)
'dreadful older phony' is the wordplay.
'dreadful' indicates anagramming the letters.
'older'+'phony'='olderphony'
'olderphony' with letters rearranged gives 'POLYHEDRON'.
(Other definitions for polyhedron that I've seen before include "Plane-faced solid" , "sugar cube perhaps" , "regular form?" .)