(i) the diameter of any triangle of perimeter two is at least 2/3
(ii) the thickness of any triangle of perimeter two is at most 1/3
(iii) the diameter of any regular hexagon cover for the family of all triangles
of perimeter two is at least one
and
(iv) the thickness of any regular hexagon cover for the family of all triangles
of perimeter two is at least 3/2 .