  (2) KS now construct another quite complicated KS diagram  Γ2  in the following way. They consider a realization of  Γ1  for an angle  θ=18°  &lt; sin−1(1/3). Now they choose three orthogonal points p0, q0, r0 and space interlocking copies of  Γ1  between them such that every instance of point a9 of one  copy of  Γ1  is identified with the instance of a0 of the next copy. In this way five interlocking copies of  Γ1  are spaced between p0 and q0 and all five instances of a8 are identified with r0 (likewise five such interlocking copies are spaced between q0 and  r0, identifying all copies of a8 with p0,  and between p0 and r0, identifying all copies of  a8 with q0). That  Γ2  is constructible is borne out directly by the construction itself. Spacing out five copies of Γ1 with angles  θ=18°  between instances of a0  will space out an angle of 5x18° = 90° which is exactly what is required. Moreover, wandering from one copy of  Γ1  to the next between, say, p0 and q0 is equivalent to a rotation by 18° of the copy about the axis through the origin and r0, which evidently conserves the orthogonality between the points a0 and a9 of the copy and r0.