Csu={{1/3,-1,5/3},{-1/3,1/2,5/6},{1/3,1/2,1/6}}

MatrixForm[Csu]

XX={3 As+At+Au,At-Au,At+Au}

Csu.XX // Simplify

Ctu={{1,0,0},{0,-1,0},{0,0,1}}

MatrixForm[Ctu]

Cst={{1/3,1,5/3},{1/3,1/2,-5/6},{1/3,-1/2,1/6}}

MatrixForm[Cst]

Cst.XX // Simplify

Clear[nineJSymbol]
nineJSymbol[{j1_,j2_,j3_},{j4_,j5_,j6_},{j7_,j8_,j9_}]:=Module[{kmin,kmax},kmin=Max[{Abs[j1-j9],Abs[j4-j8],Abs[j2-j6]}];
kmax=Min[{Abs[j1+j9],Abs[j4+j8],Abs[j2+j6]}];
Sum[(-1)^(2 k) (2 k+1) SixJSymbol[{j1,j4,j7},{j8,j9,k}] SixJSymbol[{j2,j5,j8},{j4,k,j6}] SixJSymbol[{j3,j6,j9},{k,j1,j2}],{k,kmin,kmax}]]

Csubasic=Table[nineJSymbol[{1,1,It},{1,1,It},{Is,Is,0}](-1)^(Is+It)*(2 It+1) Sqrt[(2 Is+1) (2 It+1)],{Is,0,2},{It,0,2}] ;

Csubasic-Csu // Simplify

Cstbasic=Transpose[(Table[(-1)^(d+c)(2 c+1) SixJSymbol[{1,1,c},{1,1,d}],{c,0,2},{d,0,2}])] // Simplify;

Cstbasic-Cst // Simplify

Transpose[(Table[(-1)^(c+d)( 2c+1) SixJSymbol[{1,1/2,(2d+1)/2},{1/2,1,c}],{c,0,1},{d,0,1}])] // Simplify// MatrixForm

Transpose[(Table[(-1)^(d+c)(2 c+1) SixJSymbol[{1/2,1/2,c},{1/2,1/2,d}],{c,0,1},{d,0,1}])] // Simplify// MatrixForm

ContourPlot[{(s-4)(t-16)-64==0,(t-4)(s-16)-64==0},{s,-60,60},{t,-60,60}]

?HeavysideThetha

p1=ContourPlot[{HeavisideTheta[-t]((s-4)((4-s-t)-16)-64)==0,((4-s-t-4)(s-16)-64)HeavisideTheta[-t]==0, t==-32},{s,-60,60},{t,-60,60}]

p2=ContourPlot[{HeavisideTheta[-s](((4-t-s)-4)(t-16)-64)==0,HeavisideTheta[-s]((t-4)((4-t-s)-16)-64)==0},{s,-60,60},{t,-60,60}]

p3=ContourPlot[{HeavisideTheta[s+t-4]((s-4)(t-16)-64)==0,HeavisideTheta[s+t-4]((t-4)(s-16)-64)==0},{s,-60,60},{t,-60,60}]

Show[p1,p2,p3,ContourPlot[{s==16},{s,-60,60},{t,-60,60},ContourStyle-> Black]]