부산대학교 도서관

A simply connected 3-dimensional polyhedron $P$ is called uniform if itsfaces are regular and the group of symmetry operations of $P$ actstransitively on its vertices. Such a polyhedron is said to be elementary ifit has simple vertices, edges and faces only. The number of intersectionsof $P$ with a ray issuing from the center of $P$ (considering the densityand orientation of its faces) defines the density of $P$. (The density of apolygon inscribed in a circle is defined as the number of intersections ofa ray issuing from the center of the circel with its oriented sides.)\parIn this paper, which is connected with a previous work of the author [sameSb. Vyp. 3 (1966), 123--129; MR0220160 (36 \#3226)], it is proved that thereexists only a finite number of elementary uniform polyhedra with non-zerodensity.