-- "start_parameters": coefficients of a quadric (q0,..,q9 such that q0*x0^2 + q1*x0*x1 + q2*x0*x2 + q3*x0*x3 + q4*x1^2 + q5*x1*x2 + q6*x1*x3 + q7*x2^2 + q8*x2*x3 + q9*x3^2 = 0) and cubic (c0,..,c19 such that c0*x0^3 + c1*x0^2*x1 + c2*x0^2*x2 + c3*x0^2*x3 + c4*x0*x1^2 + c5*x0*x1*x2 + c6*x0*x1*x3 + c7*x0*x2^2 + c8*x0*x2*x3 + c9*x0*x3^2 + c10*x1^3 + c11*x1^2*x2 + c12*x1^2*x3 + c13*x1*x2^2 + c14*x1*x2*x3 + c15*x1*x3^2 + c16*x2^3 + c17*x2^2*x3 + c18*x2*x3^2 + c19*x3^3 = 0)

-- "start_solns": tritangent planes (a0,..,a3 such that a0*x0 + a1*x1 + a2*x2 + a3*x3 = 0) with 3 points where it is tangent (x10,x11,x12,x13, x20,x21,x22,x23, x30,x31,x32,x33).

