Shape
The shape of an object can be characterized by basic geometry such as points, line, curves, plane, and so on. For an object of greater than 2 dimensions, one can always reduce the dimensions of the shape by considering the shape of a cross-section or a projection.
The cross-section of a spherical object, for example, will be circular. More complex shapes would, however, generate various curvatures depending on the type of cross-section (eg. horizontal, vertical). Because of the variation possible in taking cross-section, the orientation of the object is critical.
The shape does not depend on changes in orientation/direction. However, a mirror image could be called a different shape. Shape may change if the object is scaled differentially. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal axis. In other words, preserving axis of symmetry is important for preserving shapes.