부산대학교 도서관

A simply connected 3-dimensional polyhedron $P$ is called uniform if its faces are regular and the group of symmetry operations of $P$ acts transitively on its vertices. Such a polyhedron is said to be elementary if it has simple vertices, edges and faces only. The number of intersections of $P$ with a ray issuing from the center of $P$ (considering the density and orientation of its faces) defines the density of $P$. (The density of a polygon inscribed in a circle is defined as the number of intersections of a ray issuing from the center of the circel with its oriented sides.) \par In this paper, which is connected with a previous work of the author [same Sb. Vyp. 3 (1966), 123--129; MR0220160 (36 \#3226)], it is proved that there exists only a finite number of elementary uniform polyhedra with non-zero density.