The concept of shape is considered in abstract terms drawing on approaches outside the electoral districting literature. The concept is broken down into a series of four divergences from “compactness” relating to “elongation,” “indentation,” “separation,” and “puncturedness.” Given this conceptual framework, the use of shape measures in electoral districting is reconsidered and a new shape measure is proposed. This assesses the indentation of a district shape and is based on the internal angles within the shape. It is suggested that this measure may be particularly relevant to the evaluation of proposed new districting patterns. The technique is illustrated using proposed new Congressional Districts for Iowa.