Recent work on shape algebras and the maximal element representation produced a uniform and composable representation of shapes. This paper presents ongoing work to formulate a framework for sharing design knowledge based on shape algebras. The shape algebraic definitions are translated into Ontolingua, a framework for representing ontologies. It provides forms for defining classes, relations, functions, objects, and theories that are part of a conceptualization. The paper discusses some of the axioms and definitions of this ontology. It discusses the factors that influenced its design and the selection of its representational abstractions.