  However, although  Γ2 is constructible it is not consistently colourable. From the first step we know that a copy of  Γ1 with  θ=18°  requires that points a0 and a9 have equal colour.  Now, since a9 in one copy of  Γ1  is identical to a0 in the next copy, a9 in the second copy must have the same colour as a0 in the first. Indeed, by repetition of this argument all instances of a0 must have the same colour. Now, p0, q0, r0 are identified with points a0, so they must be either all white or all black — both of which are inconsistent with the colouring constraint that exactly one of them be white.