(* This uses the Gamma matrices as the example, with the Clifford spectrum just a point.  Was expecting a three sphrere. *)

n=4;

q=1;

r=1;

s=1;

t=1;

sigmax = {{0,1},{1,0}};

sigmay = {{0,-I},{I,0}};

sigmaz = {{1,0},{0,-1}};

I2 = IdentityMatrix[2];

AA= q*KroneckerProduct[-sigmay,sigmax];

MatrixForm[AA]

BB= r*KroneckerProduct[-sigmay,sigmay];

MatrixForm[BB]

CC= s*KroneckerProduct[-sigmay,sigmaz];

MatrixForm[CC]

DD = t*KroneckerProduct[sigmax,I2];

MatrixForm[DD]

loclzrHalf=KroneckerProduct[I*sigmax,AA -  w*IdentityMatrix[4]] +KroneckerProduct[I*sigmay,BB - x*IdentityMatrix[4]] +KroneckerProduct[I*sigmaz,CC -  y*IdentityMatrix[4]]+KroneckerProduct[I2,DD -  z*IdentityMatrix[4]];

charpoly=FullSimplify[Det[loclzrHalf]]

(*Notice this involves only  w  and R = Sqrt[x^2 + w^2 + z^2]  is the result of a
curve rotated into two more dimensions *)

curvePoly = ReplaceAll[charpoly, {y^2->0, z^2 ->0, x^2 -> R^2}]