Polygonal Aspects of Cell Faces. I. Pentagons and Hexagons as Prevailing Types

Wheeler, George E.

doi:10.1002/j.1537-2197.1962.tb14934.x

Cited by 4 publications

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Polygonal Aspects of Cell Faces. Ii. Quadrilaterals as the Prevailing Type

Wheeler¹

1962

American J of Botany

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Wheeler, George E. (Brooklyn Coll., Brooklyn, New York.) Polygonal aspects of cell faces. II. Quadrilaterals as the prevailing type. Amer. Jour. Bot. 49(4): 355–362. Illus. 1962.—Quadrilateral faces are abundant and even predominant among the faces of certain types of cells. Data taken from the literature and several original samples were studied to define the conditions which foster large numbers of quadrilaterals. The presence of free faces (cells on air spaces) profoundly affects cell‐face distributions. There is a great excess of quadrilaterals on cells with 2 free faces on opposite sides (cells of single layers). Among cells with 1 free face (cells of epidermises), pentagonal faces usually surpass quadrilateral faces, although they are just about equal in a few samples. Intermediate ratios of the 2 face types occur in samples which include cells having faces touching 1 free face, mixed with cells having faces between 2 free faces. The “competition” for numerical superiority shifts to pentagons vs. hexagons, among cells comprising internal tissues (cells in contact on all sides with other cells). With respect to epidermises, the relative size of epidermal and of subepidermal cells strongly influences the relative numbers of quadrilaterals and pentagons. A marked trend toward quadrilaterals may also be found in connection with a quite different set of cell relationships: if 2 layers of elongated cells occur together, and if their long axes are mutually perpendicular, then a “checkerboard” pattern may result. This arrangement favors large numbers of quadrilateral faces; in some samples, they may even dominate. It is suggested that certain modifications of this pattern may generate large numbers of triangular and of lenticular (lens‐shaped) faces. Varying patterns of cell division are considered to be primarily responsible for changes in cell‐face distributions and for changes in predominating face types.

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Polygonal Aspects of Cell Faces. Ii. Quadrilaterals as the Prevailing Type

Wheeler¹

1962

American J of Botany

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Polygonal Aspects of Cell Faces. Iii. Cell Size, Cell Division, and Cell Face Distributions

Wheeler

1963

American J of Botany

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Wheeler, George E. (Brooklyn Coll., Brooklyn, New York.) Polygonal aspects of cell faces. III. Cell size, cell division, and cell face distributions. Amer. Jour. Bot. 50(8): 747–754. Illus. 1963.—The effects of cell size differences on cell face (polygon type) distributions, and the relationship of cell division to these effects were investigated, using published and original data. Only “relative” size was considered, i.e., the size of a body compared with the sizes of contiguous bodies. A preliminary study of mixtures including 2 sizes of nonliving bodies (bubbles or shot) showed that, with increase in number of smaller bodies relative to larger, 4‐ and 5‐gons decrease and 6‐gons increase on both large and small bodies (except for 5‐gons on small bubbles). Since the cited papers on cells generally include no volume measurements, cell size was assumed to be proportional to number of faces; therefore, the cells from each sample were pooled in 3 groups of different ranges as to number of faces per cell. This device made evident the 4‐ and 5‐gon decreases and the 6‐gon increases with increasing size, but only in certain samples;‐ marked exceptions occurred among others. New data from 2 original samples showed, in general, the correlations described above, but again then; were exceptions. Discrepancies were found to arise from variable division patterns which affect face types both directly, and indirectly through division effects on cell size. It was concluded that relative size is generally less important in determining cell face distributions than are the more direct cell division events, and that size difference effects can be detected only if the other events operate minimally.

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