Globular proteins are a critically important component of the network of life. We recently proposed a simple coarse-grained model (Hoang et al 2004 Proc. Natl Acad. Sci. USA 101 7960, Banavar et al 2004 Phys. Rev. E 70 041905), which incorporates in a minimal way several physico-chemical features of globular proteins (GPs), such as the inherent anisotropy of a chain molecule and the geometrical and energetic constraints at the Cα description level imposed by hydrogen bonds, sterics, and hydrophobicity. Here, we provide a detailed description of the phase diagram of a 48-bead homopolymer chain, showing the existence and the robustness of a marginally compact phase in which the amount of degeneracy in low energy conformations is greatly reduced and the corresponding conformations exhibit a high amount of secondary structure content, thus resembling the native state folds of GPs. These results are obtained for chain lengths comparable to small real GPs and give further support to the hypothesis that GPs lie in a marginally compact phase in which the free energy landscape is pre-sculpted by geometry and symmetry.