 The sum of the face angles of any polyhedron is equal to four right angles taken as many times, less two, as the polyhedron has vertices.  Solid Geometry - Page 338by William Betz, Harrison Emmett Webb - 1916 - 178 pagesFull view - About this book
 | William Betz - Geometry - 1916 - 536 pages
...dodecahedron and of the regular icosahedron may be constructed. Make each edge of the solids about two inches. 8. Complete the following table, which summarizes...the sphere, the cylinder, and the cone, are bounded by surfaces all of which are not plane. Such surfaces are called curved surfaces. If a line-segment... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...present, so that adding the last face does not increase the number of edges or vertices. 781. THEOREM. The sum of the face angles of any polyhedron is equal...many times, less two, as the polyhedron has vertices. Let E denote the number of edges, V the number of vertices, F the number of faces, and S the sum of... | |
 | Thomas J. Foster - Coal mines and mining - 1916 - 1230 pages
...faces; and the icosahedron with twenty triangular faces. 41. The sum of all the angles of the faces of any polyhedron is equal to four right angles taken as many times as the polyhedron has vertices less two. 42. The center of any regular polyhedron and of-its circumscribed... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...2 = V + F. QED REMARK. This theorem is commonly known as Euler's Theorem. * Proposition 281 Theorem The sum of the face angles of any polyhedron is equal to four right angles taken as many times as the polyhedron has vertices less two. Hypothesis. Let S denote the sum of the face A, and V the... | |
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