Γ2 is not consistently colourable.

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 bla