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Download PDF by A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B.: Convex Polyhedra

By A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B. Sossinsky

ISBN-10: 3540231587

ISBN-13: 9783540231585

Convex Polyhedra belongs to the classics in geometry. There easily is not any different ebook that offers with a number of the points of the idea of three-d convex polyhedra in a related method, and in anyplace close to its element and completeness. it's a definitive resource of the classical box of convex polyhedra and comprises the to be had solutions to the query of the information which can uniquely make certain a convex polyhedron. this query matters all facts pertinent to a polyhedron, e.g. the lengths of edges, components of faces, etc.

This very important and obviously written publication comprises the fundamentals of convex polyhedra and collects the main basic lifestyles theorems for convex polyhedra which are proved through a brand new and unified technique. it's a tremendous resource of rules for college students.

The English version comprises a variety of reviews in addition to additional fabric and a entire bibliography through V.A. Zalgaller to carry the paintings brand new. furthermore, similar papers by way of L.A.Shor and Yu.A.Volkov were extra as vitamins to this ebook.

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Extra resources for Convex Polyhedra

Example text

29). This means that, together with the rays N1 and N2 , the angle W includes the planar angle between them. Therefore, the angle W is convex. 15 The endpoints must be deleted, since they are vertices of the polyhedron and their spherical images are spherical polygons. , about a face whose sides and vertices are deleted. 40 1 Basic Concepts and Simplest Properties of Convex Polyhedra N N1 N2 A Q Q2 Q1 Fig. 29 The faces of W are formed by the normals of the planes that touch the polyhedron along the edges adjacent to A.

If the point Am is contained in P , then its presence does not change the convex hull. In particular, it is obvious that Am cannot be a vertex. Now, assume that the point Am does not lie in P (Fig. 16). Drawing all straight line segments from Am to every point of P , we obtain a polyhedron P1 which is composed of pyramids with the common vertex Am and with bases 24 1 Basic Concepts and Simplest Properties of Convex Polyhedra the faces of the polyhedron P . The polyhedron P1 is certainly contained in the convex hull of the set of all the points A1 , A2 , .

Indeed, the movement of C along c corresponds to the rotation of the ray O C in the plane (O , c ). Hence, the planes perpendicular to the ray pass always through the ray O C perpendicular to the plane (O , c ). However, this means that the straight lines corresponding to C pass through C . The described correspondence between straight lines and points in the plane R is called the polar correspondence (with respect to the unit circle centered at O). , with the endpoint of a vector c from the origin O we associate the plane cx = 1.

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Convex Polyhedra by A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B. Sossinsky

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