The **polygons** adopted were of 20 or more sides approximating to a circular form.

These have faces which are all regular **polygons**, but not all of the same kind, while all their solid angles are equal.

Partial **Polygons** of Resistance.In a structure in which there are pieces supported at more than two joints, let a polygon be con-.

" Regular polyhedra " are such as have their faces all equal regular **polygons**, and all their solid angles equal; the term is usually restricted to the five forms in which the centre is singly enclosed, viz.

They bear a relation to the Platonic solids similar to the relation of " star **polygons** " to ordinary regular **polygons**, inasmuch as the centre is multiply enclosed in the former and singly in the latter.

- These solids are characterized by having all their angles equal and all their faces regular **polygons**, which are not all of the same species.

In drawing these **polygons** the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

- These solids have all their faces equal regular **polygons**, and the angles at the vertices all equal.

Hero's expressions for the areas of regular **polygons** of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.

The latter, as we know, calculated the perimeters of successive **polygons**, passing from one polygon to another of double the number of sides; in a similar manner Gregory calculated the areas.

As regards the funicular diagram, let LM be the line on which the pairs of corresponding sides of the two **polygons** meet, and through it draw any two planes w, w.

And the corresponding **polygons** in the other figure by the same letters; a line joining two points A, B in one figure will then correspond to the side common to the two **polygons** A, B in the other.

The stresses produced by extraneous forces in a simple frame can be found by considering the equilibrium of the various joints in a proper succession; and if the graphical method be employed the various **polygons** of force can be combined into a single force-diagram.