A model is presented for the arrangement of alpha-helices in globular proteins. In the model, helices are placed on certain ribs of "quasi-spherical" polyhedra. The polyhedra are chosen so as to allow the close packing of helices around a hydrophobic core and to stress the collective interactions of the individual helices. The model predicts a small set of stable architectures for alpha-helices in globular proteins and describes the geometries of the helix packings. Some of the predicted helix arrangements have already been observed in known protein structures; others are new. An analysis of the three-dimensional structures of all proteins for which co-ordinates are available shows that the model closely approximates the arrangements and packing of helices actually observed. The average deviations of the real helix axes from those in the model polyhedra is +/- 20 degrees in orientation and +/- 2 A in position (1 A = 0.1 nm). We also show that for proteins that are not homologous, but whose helix arrangements are described by the same polyhedron, the root-mean-square difference in the position of the C alpha atoms in the helices is 1.6 to 3.0 A.