Tetradecahedral-shaped cells in multiple organisms allow for maximal packing space while also resisting compression.

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The leaf stalks of Nasturtiums resist compression via orthotetrakaidecahedron-shaped support cells.

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“The compressive core [of herbaceous stems] holds especial interest, at least to me. In a freshman botany course I dutifully memorized the ‘fact’ that the inner, thin-walled, cells (parenchyma) of such a stem had a particular shape–a so-called orthotetrakaidecahedron, a fourteen-sided solid with eight six-edged faces and six four-edged faces (fig. 20.3). Only years later did I read D’Arcy Thompson (1942) and get an idea of the significance of that shape. If a set of distortable spheres of equal size are squeezed together so they completely fill some large volume, each will (ideally at least) take on this particular shape. It’s the shape that permits each to expose the minimum surface area. So the peculiar shape of these cells supports the idea that they’re being squeezed and thus that they function as a compression-resisting core. Only thin cell walls are needed–pressure shouldn’t differ among the individual cells, and most of the motile animal systems lack any partitions at all. Still, these flimsy-looking cells have a crucial supportive function. The fourteen-sided shape, incidentally, idealizes somewhat–the real cells actually vary a bit (Hulbary 1944). Wainwright et al. (1976) mention this system, using the Nasturtium petiole (leaf stem) as an example.” (Vogel 2003:412-413)

Comparative Biomechanics: Life's Physical World, Second EditionPrinceton University PressJune 17, 2013
Steven Vogel

“In a series of painstaking and masterly researches Lewis (1923, 1925) has shown that cells of the elder pith, of human adipose tissue, and of the epithelium of the human oral cavity
have on an average fourteen faces, and therefore are or tend to be tetrakaidecahedra. Some cells show a striking alternation of hexagonal and quadrilateral faces, suggesting the ” plane-faced isotropic ” or ” orthic ” tetrakaidecahedron that Kelvin (1887, 1894a, 1894b, 1904) described. Kelvin stated that space can be filled with equal and similar orthic tetrakaidecahedra, and that, further, they do not possess the unstable tetrahedral angles of the rhombic dodecahedron. And Lewis (1925, 1926) gives data to show that the orthic tetrakaidecahedron has less surface per unit of volume than the rhombic dodecahedron. Unit volumes of this configuration approach then as nearly to the condition of maximum volume with minimum surface as this can be achieved by aggregates of equal and similar units without spaces between” (Matzke 1927:341).

Journal article
An Analysis of the Orthic TetrakaidecahedronBulletin of the Torrey Botanical Club, Vol. 54, No. 4 (Apr., 1927), pp. 341-348Edwin B. Matzke

Journal article
Modelling the orthic tetrakaidecahedronTorreya, Vol. 31, No. 5 (September-October, 1931), pp. 129-135December 29, 2017
Edwin B. Matzke

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