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TrigGaussRuleInfo[{rule_,numer_},point_] := Module [
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  If [ p ==  1, info={{1/3,1/3,1/3},1}];
  
  If [ p ==  3, info={{1,1,1}/6,1/3}; info[[1,i]]=2/3];
  
  If [ p == -3, info={{1,1,1}/2,1/3}; info[[1,i]]=0];
  
  If [ p ==  6, g1 = (8-Sqrt[10]+Sqrt[38-44*Sqrt[2/5]])/18;
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      If [ i < 4, info={{g1,g1,g1}, (620+Sqrt[213125-53320*Sqrt[10]])/3720};
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      If [ i > 3, info={{g2,g2,g2}, (620-Sqrt[213125-53320*Sqrt[10]])/3720};
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  If [ p == -6,
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      If[i>3, info={{1,1,1}/2,1/30}; info[[1,i-3]]=0]];
      
  If [ p == 7, g1=(6-Sqrt[15])/21;
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             info[[1,i]] = 1-2*g1];
     If[i>3&&i<7, info={{g2,g2,g2},(155+Sqrt[15])/1200};
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     If[i==7, info={{1/3,1/3,1/3},9/40}]];
     
  If [ p == 12,
     g1=0.063089014491502228340331602870819157;
     g2=0.249286745170910421291638553107019076;
     g3=0.053145049844816947353249671631398147;
     g4=0.310352451033784405416607733956552153;
     If [ !numer, {g1,g2,g3,g4}=Rationalize[{g1,g2,g3,g4},eps]];
      w1=(30*g2^3*(4*g3^2+(1-2*g4)^2+4*g3*(-1+g4))+
          g3^2*(1-15*g4)+(-1+g4)*g4-g3*(-1+g4)*(-1+15*g4)+
          2*g2+(1+60*g3*g4*(-1+g3+g4))-6*g2^2*(3+10*(-1+g4)*g4+
          10*g3^2*(1+3*g4)+10*g3*(-1+g4)*(1+3*g4)))/
         (180*(g1-g2)*(-(g2*(-1+2*g2)*(-1+g3)*g3)+(-1+g3)*(g2-2*g2^2-
          2*g3+3*g2*g3)*g4-(g2*(-1+2*g2-3*g3)+2*g3)*g4^2+
          2*g1^2*(g2*(-2+3*g2)+g3-g3^2+g4-g3*g4-g4^2)+
          g1*(-4*g2^2+(-1+g3)*g3+(-1+g3)*(1+3*g3)*g4+(1+3*g3)*
          g4^2-2*g2*(-1+g3^2+g3*(-1+g4)+(-1+g4)*g4))));
      w2=(-1+12*(2-3*g1)*g1*w1+4*g3^2*(-1+3*w1)+4*g3*(-1+g4)*(-1+3*w1)+
          4*(-1+g4)*g4*(-1+3*w1))/(12*(g2*(-2+3*g2)+g3-g3^2+g4-g3*g4-g4^2));
      w3=(1-3*w1-3*w2)/6;
      If [ i<4, info={{g1,g1,g1},w1}; info[[1,i]] = 1-2*g1];
      If [ i>3&&i<7, info={{g2,g2,g2},w2}; info[[1,i-3]]=1-2*g2];
      If [ i>6, {j,k,l}=jkl[[i-6]]; info={{0,0,0},w3};
        info[[1,j]]=g3; info[[1,k]]=g4;info[[1,l]]=1-g3-g4]];
        
  If [ numer, Return[N[info,20]], Return[Simplify[info]]];
];
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