This investigation originated with a question about inversive planes, which was answered in [19] and [20]. Those results, as well as their analogues for Laguerre and Minkowski planes are special cases of the main result of the present paper; but we are now concerned with a more general class of objects here called locally projective-planar lattices in which some properties particular to one or more of the above-mentioned planes are dispensed with. Our main theorem will be introduced in Sect. 2; we begin here with some discussion of the classical examples. An inversive plane is an incidence structure (see Chap. II) ~ = (0, off) (elements of (g are called circles) which satisfies: (0) Circles are nonempty. (1) For each P~(9, ~p is an affine plane (where J e is the internal structure whose points are the points of (9 other than P, whose blocks are the circles of c~ which contain P, and whose incidence is that inherited from J ) . The order of J is the (common) order of the affine planes Jp . Inversive planes arise quite naturally in geometry in the following way. Let K be a skewfield and (9 an ovoid in PG(3, K). (I.e., (9 is a set of points satisfying: (1) no three points of (9 are collinear, and (2) if P~(9, then the union of all lines meeting (9 only in P is a plane. PG(3,K) denotes three-dimensional projective space over K.) Then the following incidence structure, ~r is an inversive plane: The points of J((9) are the points of (9. The circles of J((9) are those planes which meet (9 in more than one point. Incidence is inclusion. An inversive plane is said to be egglike 1 if is isomorphic to some J((9). * Supported in part by ONR Contract ~N00014-76-C-0366 1 This term is due to Dembowski and Hughes [131