Rectangular Euler Diagrams and Order Theory

This paper discusses the relevance of order-theoretical properties, such as order dimension, for determining properties of Euler diagrams, such as whether a given poset can be represented with or without shading. The focus is on linear, tabular and rectangular Euler diagrams with shading and without split attributes and constructions with subdiagrams and embeddings. Euler diagrams are distinguished from geometric containment orders. Basic layout strategies are suggested.