## Polyhedra Sentence Examples

- (4) On the inscribing of each of the five regular
**polyhedra**in a sphere. - The general theory of
**polyhedra**properly belongs to combinatorial analysis. - Of lost works by Archimedes we can identify the following: (I) investigations on
**polyhedra**mentioned by Pappus; (2) Archai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) Peri zygon, On balances or levers; (4) Kentrobarika, On centres of gravity; (5) Katoptrika, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) Ephodion, a Method, mentioned by Suidas; (7) Peri sphairopeoia, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens. - He shows how to inscribe the five regular
**polyhedra**within it. - Incidentally Pappus describes the thirteen other
**polyhedra**bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere. - Stevinus was the first to show how to model regular and semiregular
**polyhedra**by delineating their frames in a plane. - If we project both
**polyhedra**orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel. - " 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. - The Platonic solids, while the four
**polyhedra**in which the centre is multiply enclosed are referred to as the Kepler-Poinsot solids, Kepler having discovered three, while Poinsot discovered the fourth. - Another group of
**polyhedra**are termed the " Archimedean solids," named after Archimedes, who, according to Pappus, invented them. - " A The following Table gives the values of A, V, R, r for the five
**Polyhedra**: - Kepler-Poinsot**Polyhedra**. - A connexion between the number of faces, vertices and edges of regular
**polyhedra**was discovered by Euler, and the result, which assumes the form E + 2' = F ± V, where E, F, V are the number of edges, faces and vertices, is known as Euler's theorem on**polyhedra**. - The following table gives these constants for the regular
**polyhedra**; n denotes the number of sides to a face, n 1 the number of faces to a vertex: - Archimedean Solids. - The interrelations of the
**polyhedra**enumerated above are considerably elucidated by the introduction of the following terms: (1) Correspondence. - Two
**polyhedra**correspond when the radii vectores from their centres to the mid-point of the edges, centre of the faces, and to the vertices, can be brought into coincidence. - Two
**polyhedra**are reciprocal when the faces and vertices of one correspond to the vertices and faces of the other. - Hemihedral forms are of special importance in crystallography, to which article the reader is referred for a fuller explanation of these and other modifications of
**polyhedra**(tetartohedral, enantiotropic, &c.). - The correspondence of the faces of
**polyhedra**is also of importance, as may be seen from the manner in which one polyhedron may be derived from another. - The determination of the number of different
**polyhedra**of n faces, i.e.