Pick a root of x^3 - 7 x +7 =0. I'll use ~1.3569 Take the dot product of {1,x,x^2} with the following, then take the sign-carry square root (as in sqrt(4) = 2, sqrt(-4)=-2). You'll get a heptagon. v = {{{0, 0, 0}, {4, 0, 0}}, {{7, -2, -1}, {-3, 2, 1}}, {{7, -1, -1}, {3, -1, -1}}, {{-7, 3, 2}, {-11, 3, 2}}, {{7, -3, -2}, {-11, 3, 2}}, {{-7, 1, 1}, {3, -1, -1}}, {{-7, 2, 1}, {-3, 2, 1}}}/4; Pick a root of x^3 - 9 x +9 =0. I'll use ~1.18479 Take the dot product of {1,x,x^2} with the following, then take the sign-carry square root (as in sqrt(4) = 2, sqrt(-4)=-2). You'll get a nonagon. v = {{{0,0,1},{-12,0,1}},{{9,0,0},{-3,0,0}},{{18,-3,-2},{-6,3,2}}, {{0,3,1},{12,-3,-1}},{{0,0,0},{12,0,0}},{{0,-3,-1},{12,-3,-1}}, {{-18,3,2},{-6,3,2}},{{-9,0,0},{-3,0,0}},{{0,0,-1},{-12,0,1}}}; In short x^3 = 7 (x -1) makes a 7-gon. x^3 = 9 (x -1) makes a 9-gon. Some similar things at https://math.stackexchange.com/questions/2609505/the-heegner-polynomials --Ed Pegg Jr