Objects with icosahedral symmetry (I-h) bear a special fascination; natural examples are rare, but include radiolaria(1) and virus particles (virions)(2). The discovery(3) of C-60, a molecule in the shape of a truncated icosahedron with a symmetry, has aroused widespread interest. In 1962, Mackay(4) described a radiating packing of spheres in I-h symmetry, in which the centres of successive shells of spheres lie on the surfaces of icosahedra. There has been extensive investigation of the conditions under which such packing might be realized in assemblies of atoms or of molecules such as C-60 (ref. 5). Here we report the preparation, at high temperatures and pressures, of boron suboxide (B6O) in which the preferred form of the material is as macroscopic, near-perfect, regular icosahedra, similar to the multiply-twinned particles observed in some cubic materials. A major difference is that B6O has a rhombohedral structure that nearly exactly fits the geometrical requirements needed to obtain icosahedral twins. These icosahedral particles have a structure that can be described as a Mackay packing of icosahedral B-12 units, and thus has long-ranged order without translational symmetry.