If in fact we take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the "conjugate lines" of those of the former.
The points thus obtained are evidently the vertices of a polyhedron with plane faces.
If we take anypolyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former.
The lattice-shell of the Orosphaerida is usually spherical, or an endospherical polyhedron (Pl.
From the elevated corners of the polyhedron arise thirty-two radial spines (twelve in the central points of the pentagons, twenty in the meeting corners of every three pentagons).
From the elevated corners of the polyhedron arise twenty-four to thirty radial spines, which are three-sided prismatic or nearly cylindrical, about as long as the radius of the shell, and covered with long curved bristles.
From the elevated corners of the polyhedron arise thirty to forty radial spines, which are longer than the diameter of the shell, densely covered with curved bristles and three-sided prismatic, with three spirally convoluted edges.
The theorem asserts that in any convex polyhedron the number of edges increased by two is equal to the number of vertices increased by the number of faces.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "polyhedron" in a variety of sentences. We hope that you will now be able to make sentences using this word.
