Universality Theorems for Inscribed Polytopes and Delaunay Triangulations

摘要: We prove that every primary basic semi-algebraic set is homotopy equivalent to the of inscribed realizations (up Mobius transformation) a polytope. If is, moreover, open, it additionally, homotopy) retract realization space some neighborly (and simplicial) also show all algebraic extensions $${\mathbb {Q}}$$Q are needed coordinatize polytopes. These statements polytopes exhibit Mnev universality phenomenon. Via stereographic projections, these theorems have direct translation for Delaunay subdivisions. In particular, realizability problem triangulations polynomially existential theory reals.