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Mou, Zhao, and McNamara (2007) proposed the "intrinsic model of human spatial memory," which posits that a viewer's memory of an array of objects will exhibit a preferred direction that is aligned with an intrinsic axis of the array. They defined intrinsic axes as salient axes created in part by the physical (geometric) properties of the array. To date, these geometric characteristics have received little research attention. We begin such an endeavor by evaluating the role of symmetry and orthogonality (i.e., number of right angles in an array of objects) in spatial memory. Participants viewed a layout of objects from a single (Experiment 1) viewpoint or 2 (Experiment 2) viewpoints and then judged relative directions within the layout from memory. Orthogonality and symmetry were associated with decreased reliance on egocentric reference systems but were qualified by a generally greater reliance on egocentric reference frames than is common in the literature. Indeed, for only 1 array--a highly orthogonal and symmetric one--did participants consistently respond nonegocentrically. We suggest that overuse of this array in the literature has led to an overestimation of the importance of allocentricity in spatial memory. [ABSTRACT FROM AUTHOR]