By Kollar J., Lazarsfeld R., Morrison D. (eds.)
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Additional resources for Algebraic Geometry Santa Cruz 1995, Part 2
On the other hand, in the polygons ABC DE and A' B'C' D' E', corresponding sides are congruent (as opposite sides of parallelograms), and correspond1 Polyhedm (or polyhedrom;) is the plural of polyhedron. 29 Chapter 2. POLYHEDRA 30 ing angles are congruent (as angles with respectively parallel and similarly directed sides). T herefore these polygons are congruent. Thus, a prism can be defined as a polyhedron two of whose faces are congruent polygons with respectively parallel sides, and all other faces are parallelograms connecting the parallel sides.
Similarity of polyhedra 53 point A' homothet ic to A lies not on the ray SA, but on the extension of it beyond the center S. It is not hard to see that in the case of a negative homothety coefficient , the figure homothetic to a given polyhedral angle with respect to its vertex is the polyhedral angle symmetric to the given one in the sense of §49. 71. Lemma. Two geometric figures homothetic to a given one with the same homothety coefficients but with respect to two different centers are congruent to each other.
A straight segment connecting any two vertices, which do not lie in the same face , is called a diagonal of the polyhedron. The smallest number of faces a polyhedron can have is four. Such a polyhedron can be cut out of a trihedral angle by a plane. e. lie on one side of the plane of each of its faces. 52. Prisms. Take any polygon ABODE (Figure 39), and through its vertices, draw parallel lines not lying in its plane. Then on one of the lines, take any point (A') and draw through it t he plane parallel to t he plane ABODE, and also draw a plane through each pair of adjacent parallel lines.
Algebraic Geometry Santa Cruz 1995, Part 2 by Kollar J., Lazarsfeld R., Morrison D. (eds.)