Sponges

摘要

The geometric features of sponges, which describe polycontinuous morphologies, are discussed. The focus is on 3-periodic surfaces, which have an underlying 3-d lattice. Definitions and explanations of a range of concepts from non-euclidean geometry, topology and differential geometry are used to derive local and global features of smoothly curved sponges, facetted polyhedral sponges and reticulating networks of edges on these forms.