Unprojection theory aims to analyze (and construct) complicated commutative rings in terms of simpler ones. The talk will be about joint work in progress with Christos Athanasiadis (Athens) and Janko Boehm (Saarbruecken) that relates, on the algebraic level of Stanley--Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes with the unprojection of type Kustin--Miller.