Irregular Polygons

As used today, the word linen is descriptive of a class of woven textiles used in homes. Linens were manufactured almost exclusively of fibres from the flax plant Linum usitatisimum. Today flax is a prestigious, expensive fibre and only produced in small quantities. Flax fibres can be identified by their typical nodes, which account for the flexibility and texture of the fabric. The cross-section of the fibre is made up of irregular polygonal shapes, which contribute to the coarse texture of the fabric. When adequately prepared, linen has the ability to absorb and lose water rapidly. It can gain up to 20% moisture without feeling damp. 

If this condition is not met, the constrained mixture space will resemble an irregular polygon as in Figure 2.35(b). An example is illustrated in Table 2.40(b). 

The mixture design is normally represented as an irregular polygon, with, in this case, six vertices. Calculate the percentage of each factor at the six coordinates. 

As pointed out in Section 7, the plastio foam cells have a very complex shape, most frequently that of irregular polygons, which makes the use of the above formulas too cumbersome nevertheless, the order of the specific surface value given by the equations is correct. 

The test site, shaped like an irregular polygon and familiarly called the polygon, is a 19,000 km" zone in the northeast of the newly independent Republic of Kazakhstan, 800 km north of the Kazakh capital Alma-Ata. The zone lies southwest of the Irtysh River which flows into Kazakhstan from China and which for a short stretch, where it veers sharply northwards on its way to join the Ob River in Siberia, forms part of the polygon boundary (see Fig. 10.16). The USSR conducted 465 nuclear tests at three locations called technical areas within the polygon over a period of 40 years (1949-1989) for military and peaceful purposes. 

Flax is stained blue by zinc chloride-iodine reagent (see Section 8.5.6), as are all other cellulose fibres. In addition the typical V- and X-shaped transverse structures can be seen more clearly. Differentiation from hemp can be made by means of a cross-sectional sample. Flax shows clearly visible irregular polygons with lumen, hemp shows relatively indistinct and often conglomerate structures. 

Catalan polyhedron A polyhedron that has a duality relationship with an Archimedean polyhedron, with all faces of identical irregular polygons and more than one set of vertices. 

Fig. 3.6. An irregular polygon has a centre of symmetry at the point P. Each point is equidistant from P, from the corresponding point on the opposite side of centre point P. If every point within a body can be inverted through a centre then the body is transformed to self coincidence by the inversion...

A concept first used in Ref. 7, where it was called an irregular polygon. An alternative analytical procedure for computing the polygon s coordinates can be found there. 

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