On the Newton number of rectangles

The Newton number N(K) of a convex body K is the maximum number of disjoint congruent copies of K that can be arranged around K such that all touch K without having interior points in common. If R = R(a,b) is a rectangle with edge lengths a and b and a/b = n + r, n is an element of N, 0 less than or equal to r < 1 then 2n + 6 less than or equal to N(R) less than or equal to 2n + 7. Moreover, if 0 less than or equal to r less than or equal to 1/2 then N(R) = 2n + 6 and if root 3/2 = 0.8660... less than or equal to r < 1 then Ar(R) = 2n + 7.