Polygonal Type Research Articles

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

Wheeler, George E. (Brooklyn Coll., Brooklyn, N. Y.) Polygonal aspects of cell faces. I. Pentagons and hexagons as prevailing types. Amer. Jour. Bot. 49(3): 246–252. Illus. 1962.—Different types of cell faces, classified as to polygon type (i.e., number of sides per face), may predominate in different samples of internal cells and of internal tissues; no single face type is exclusively predominant in all tissues. Pentagons usually are the most numerous type in the cell samples reported in the literature, but hexagons exceed them in some samples. Generally, these 2 “compete” for numerical supremacy. Perpetuation of an already-established, face-type dominance was studied, using data from the literature and from original diagrams. Cell-division orientation, i.e., the location and the relative positioning of new cell-division walls, was found to be the prime factor in maintaining the preponderant type. The polygon nature of the new wall is an additional, but less important, factor. Typical division events tend to favor pentagonal faces; but with an increase in cell division “regularity,” hexagons begin to rise in numbers. During the early stages in tissue differentiation, while mitosis is still occurring, one face type may replace another as the predominating type. Such a shift may be associated with the developmental characteristics of that tissue.

POLYGONAL ASPECTS OF CELL FACES. I. PENTAGONS AND HEXAGONS AS PREVAILING TYPES

Wheeler, George E. (Brooklyn Coll., Brooklyn, N. Y.) Polygonal aspects of cell faces. I. Pentagons and hexagons as prevailing types. Amer. Jour. Bot. 49(3): 246–252. Illus. 1962.—Different types of cell faces, classified as to polygon type (i.e., number of sides per face), may predominate in different samples of internal cells and of internal tissues; no single face type is exclusively predominant in all tissues. Pentagons usually are the most numerous type in the cell samples reported in the literature, but hexagons exceed them in some samples. Generally, these 2 “compete” for numerical supremacy. Perpetuation of an already‐established, face‐type dominance was studied, using data from the literature and from original diagrams. Cell‐division orientation, i.e., the location and the relative positioning of new cell‐division walls, was found to be the prime factor in maintaining the preponderant type. The polygon nature of the new wall is an additional, but less important, factor. Typical division events tend to favor pentagonal faces; but with an increase in cell division “regularity,” hexagons begin to rise in numbers. During the early stages in tissue differentiation, while mitosis is still occurring, one face type may replace another as the predominating type. Such a shift may be associated with the developmental characteristics of that tissue.

CELL FACE CORRELATIONS AND GEOMETRICAL NECESSITY

As PHYSICAL entities, the cells which make up tissues are subject to certain geometrical laws operating on all such three-dimensional bodies. But one of the aims of biological investigations is the eluicidation of those phenomena peculiar to living systems as contrasted with non-living systems. If an understanding of cell form is to be useful in such studies, cell shape attributes which result from .mathematical necessity must be clearly recognized; otherwise, they may obscure the effects of the more fundamental biological processes. This is an attempt to distinguish these two groups of factors as they influence the correlations found among cell faces (classified as to polygon type). Inasmuch as the study is based on data already published, conclusions cannot properly be extended beyond the samples furnishing the data. Although such an approach limits the applicability of the results, it is possible, nevertheless, to uncover important trends which may be bases for further study. LITERATURE REVIEW.-Almost all writers on cell shape have remarked on one or another of the relations found among cell faces. But such references, especially with respect to the faces of cells completely surrounded by other cells, are brief and scattered. Even Thompson (1942), considering form in living things from a primarily mathematical point of view, said little abiout cell face correlations. The usefulness of Euler's Theorem in studies of cell faces was emphasized by Lewis (1933a, 1933b), by Marvin (1944), and by Matzke and Duffy (1956). Although almost every author has noted that larger cells tend to have more faces, this is not inevitable (Lewis, 1944; Matzke and Duffy, 1956). Lewis (1931) discussed the tendency of larger faces to have more sides, and Marvin (1939) confirmed it with actual measurements. In this connection, too, there are exceptions: Siegerman (1951) and Wheeler (1955) found that criss-crossed divisions may produce unusually small faces. Contiguity of large with small bodies has definite effects on number and on kinds of faces (Matzke, 1939, 1945; Marvin, 1944;' Mozingo, 1951; Matzke and Duffy, 1956). Cell division strongly influences a number of cell shape attributes. Dodd (1948) and Lier (1952) explained certain cell face peculiarities in terms of unequal rates of cell division among adjacent cells. Lewis (1943) and Duffy (1951) stressed the importance of regular and irregular planes of division. Criss-crossed divisionsare inseparably linked with the formation of triangles, of lensshaped faces, and of several other types (Siegerman, 1951; Wheeler, 1955; Rahn, 1956). More

Notes on Some Plant Communities in the Northern Mackenzie Basin, Canada

Selected examples illustrating a number of the plant communities in the Mackenzie District between 60⚬50' N. Lat. and 69⚬20' N. Lat., excepting mesic forest sites, are described. Five distinct moist tundra communities on sand, determined by exposure and drainage conditions, form an intimate mosaic. In the transition spruce forest farther southeast, a very large type of raised-center polygon has the center dominated by a flat stand of Cladonia and Cetraria, dotted with hummocks of Sphagnum and low ericaceous shrubs. An inland saline meadow exemplifies a habitat unique in this region. Bogs with true floating mats rarely occur; consequently, Sphagnum is far less important in low wet sites than Camptothecium, Aulacomnium, and Dicranum. Where frequent stream flooding brings in silt, and on pond borders, reed-marsh communities are very prevalent. Their dense emergent growth, dominated by Carex aquatilis, C. rostrata, or Equisetum limosum, initiates peat accumulation. Communities upon deeper organic deposits include (a) tussock-sedge low-willows, (b) ground-birch muskeg, (c) tall clumped willows, and (d) closed stands of tall willow and paper birch. These are not all related successionally. The black spruce and tamarack dominate mature bogs in both the northern transition forest of the Pre-Cambrian Shield and the Mackenzie Lowlands region. Such bogs have a shrub stratum of low, mostly ericaceous chamaephytes, and a ground cover of non-Sphagnum mosses and Equisetum scirpoides.

A Type of Polygons with a Common Centroid

A Type of Polygons with a Common Centroid

Further Observations on the Polygonal Type of Settlement in Britain

Further Observations on the Polygonal Type of Settlement in Britain

Some Factors Affecting the Development of Mud-Cracks

Some Factors Affecting the Development of Mud-Cracks