Square or take the square root. In my Substitution Tilings program at http://demonstrations.wolfram.com/SubstitutionTilings/ , I have a routine called SqrtSpace. Pictures at https://community.wolfram.com/groups/-/m/t/1679969 In the Psi Quad tiling, https://community.wolfram.com//c/portal/getImageAttachment?filename=PsiQuad.... , the algebraic number field is Psi, ψ, the https://en.wikipedia.org/wiki/Supergolden_ratio . The coordinates in the tiling are NOT in the algebraic number field of ψ, since sextics are involved. However, with a sign-preserving squaring or square root operation, all coordinates work perfectly within the algebraic number field. I expand on this more at https://blog.wolfram.com/2019/03/07/shattering-the-plane-with-twelve-new-sub... Squaring/sqrt makes coordinates elegant for extremal orchard solutions. https://blog.wolfram.com/2018/02/02/cultivating-new-solutions-for-the-orchar... Squaring makes all vertices elegant for degenerate power simplex coordinates. http://demonstrations.wolfram.com/DegeneratePowerSimplices/ "If it doesn't work, try squaring your values." -- I've heard this since college, but I didn't expect it to work so well in algebraic number fields. Is there a name for this? Ed Pegg Jr