Abstract This article focuses on the Platonic version of doctrine oikeiosis set forth by Piso in Cicero’s De finibus , Book V. The aims to show that: 1) account, while clearly having Stoic features, is also consistent with eudaemonistic character Socrates’ and Plato’s ethics; 2) replacement “assimilation god”, attested a passage Anonymous Commentary Theaetetus derives from intent remove Epicure...

Sunada’s work on topological crystallography emphasizes the role of the ‘maximal abelian cover’ of a graph X. This is a covering space of X for which the group of deck transformations is the first homology group H1(X,Z). An embedding of the maximal abelian cover in a vector space can serve as the pattern for a crystal: atoms are located at the vertices, while bonds lie on the edges. We prove th...

The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to...