J.M.C. Hutchinson 2000. Three into two doesn’t go; two-dimensional models of bird eggs, snail shells, and plant roots. Biological Journal of the Linnean Society 70:161–187.

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Some further papers of relevance to the broad theme
Roth, V.L. 1993. On three-dimensional morphometrics, and on the identification of landmark points. Pp. 41-61 in Contributions to Morphometrics (L.F. Marcus, E. Bello & A. García-Valdecasas, eds) . Museo Nacional de Ciencias Naturales CSIC, Madrid.
Cuddington, K.M. & Yodzis, P. 2000. Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model. Theoretical Population Biology 58: 259–278.
Fan, J., Liu, F., Wu, J. & Dai, W. 2003. Visual perception of female physical attractiveness. Proceedings of the Royal Society of London B 271: 347–352.
Abbott, A. 2003. Biology’s new dimension. Nature 424: 870–872. (See also the second editorial on p. 861)
Clegg, R.J. & Kreft, J.-U. 2017. Reducing discrepanceis between 3D and 2D simulations due to cell packing density. Journal of Theoretical Biology 423:26–30.
Vivancos, A., Close, G. & Tentelier, C. 2017. Are 2D space-use analyses adapted to animals living in 3D environments? A case study on a fish shoal. Behavioral Ecology 28: 485–493.
Our own paper on rates of random encounter between moving items also provides lots of examples of different relations in 3 dimensions than 2: Hutchinson, J.M.C. & Waser, P.M. 2007. Use, misuse and extensions of “ideal gas” models of animal encounter. Biological Reviews 82: 335–359.

Egg shape
Johnson et al. (2001) conduct an intraspecific comparison of egg shape, showing no relation to clutch size.

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