Toric Objects Associated with the Dodecahedron

Abstract

In this paper we illustrate a tight interplay between homotopy theory and combinatorics within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complexand real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related small cover. We nish by studying Massey products in the cohomology ring of moment-angle manifolds over the dodecahedron and how the existence of nontrivial Massey products in uences the behaviour of the Poincare series of the corresponding Pontryagin algebra