AbstractThe search for a least dense packing of spheres makes sense only under suitable restrictions because otherwise sphere packings of arbitrarily low density may be constructed. As has been shown before, the condition that all spheres have to be equal as well in their size as in their number of contacts is not such an effective restriction. A sharper condition is the demand that all spheres must have congruent patterns of contacts,i.e.that they must coincide in their first neighbourhood. The example presented here proves that also this restriction is not sufficient to avoid sphere packings with densities approaching zero.