부산대학교 도서관

We construct new polyhedra such that some of their similar or affine images can be inscribed in (or circumscribed about) every centrally symmetric convex body. One of the main theorems is as follows. If K is a centrally symmetric, three-dimensional, convex body, then either an affine-regular dodecahedron is inscribed in K or there are two affine-regular dodecahedra D and D such that nine pairs of opposite vertices of D, i = 1, 2, lie on the boundary of K. Furthermore, the remaining two vertices of D lie outside K, while the remaining two vertices of D lie inside K. [ABSTRACT FROM AUTHOR]