Составной ключ для std::map

class Vertex{
public:
    double X,Y,Z;
    Vertex(double x=0,double y=0, double z=0){X=x;Y=y;Z=z;}
    void Set(double x,double y,double z){X=x;Y=y;Z=z;}
    void print(){printf("X=%f, Y=%f, Z=%f\n",X,Y,Z);}
    double L(){return Sqrt((X*X)+(Y*Y)+(Z*Z));}
    double L(Vertex A){return Sqrt((X*X-2*X*A.X+A.X*A.X)+(Y*Y-2*Y*A.Y+A.Y*A.Y)+(Z*Z-2*Z*A.Z+A.Z*A.Z));}
    bool operator  <(double A){return (X<A && Y<A && Z<A);}
    bool operator  >(double A){return (X>A && Y>A && Z>A);}
    bool operator ==(Vertex A){return (X==A.X && Y==A.Y && Z==A.Z);}
    bool operator  <(Vertex A){return std::tie(X, Y, Z) < std::tie(A.X, A.Y, A.Z);}
    bool operator ==(double A){return (X==A && Y==A && Z==A);}
    bool operator !=(double A){return (X!=A || Y!=A || Z!=A);}
    bool operator !=(Vertex A){return (X!=A.X || Y!=A.Y || Z!=A.Z);}
    void operator +=(Vertex A){X+=A.X;Y+=A.Y;Z+=A.Z;}
    void operator +=(double A){X+=A;Y+=A;Z+=A;}
    void operator *=(Vertex A){X*=A.X;Y*=A.Y;Z*=A.Z;}
    void operator *=(double A){X*=A;Y*=A;Z*=A;}
    void operator /=(double A){X/=A;Y/=A;Z/=A;}
    void operator -=(Vertex A){X-=A.X;Y-=A.Y;Z-=A.Z;}
    void operator  =(double A){X=A;Y=A;Z=A;}
    Vertex operator *(double A){return Vertex(X*A,Y*A,Z*A);}
    Vertex operator -(Vertex A){return Vertex(X-A.X,Y-A.Y,Z-A.Z);}
    Vertex operator +(Vertex A){Vertex Res=*this;Res+=A;return Res;}
    double GetA(){return X/L();}
    double GetB(){return Y/L();}
    double GetC(){return Z/L();}
    bool Null(){if(X==0 && Y==0 && Z==0)return 1;return 0;}
    Vertex Normalize(){double l=Sqrt((X)*(X)+(Y)*(Y)+(Z)*(Z));X/=l;Y/=l;Z/=l;return *this;}
};
int main(){
    Vertex A;
    std::map<Vertex,int> C;
    C[A]=231;
}

class Vertex{
public:
    double X,Y,Z;
    Vertex(double x=0,double y=0, double z=0){X=x;Y=y;Z=z;}
    void Set(double x,double y,double z){X=x;Y=y;Z=z;}
    void print(){printf("X=%f, Y=%f, Z=%f\n",X,Y,Z);}
    double L(){return Sqrt((X*X)+(Y*Y)+(Z*Z));}
    double L(Vertex A){return Sqrt((X*X-2*X*A.X+A.X*A.X)+(Y*Y-2*Y*A.Y+A.Y*A.Y)+(Z*Z-2*Z*A.Z+A.Z*A.Z));}
    const bool operator  <(double A){return (X<A && Y<A && Z<A);}
    const bool operator  >(double A){return (X>A && Y>A && Z>A);}
    const bool operator ==(Vertex A){return (X==A.X && Y==A.Y && Z==A.Z);}
    const bool operator  <(Vertex A){return std::tie(X, Y, Z) < std::tie(A.X, A.Y, A.Z);}
    const bool operator ==(double A){return (X==A && Y==A && Z==A);}
    const bool operator !=(double A){return (X!=A || Y!=A || Z!=A);}
    const bool operator !=(Vertex A){return (X!=A.X || Y!=A.Y || Z!=A.Z);}
    void operator +=(Vertex A){X+=A.X;Y+=A.Y;Z+=A.Z;}
    void operator +=(double A){X+=A;Y+=A;Z+=A;}
    void operator *=(Vertex A){X*=A.X;Y*=A.Y;Z*=A.Z;}
    void operator *=(double A){X*=A;Y*=A;Z*=A;}
    void operator /=(double A){X/=A;Y/=A;Z/=A;}
    void operator -=(Vertex A){X-=A.X;Y-=A.Y;Z-=A.Z;}
    void operator  =(double A){X=A;Y=A;Z=A;}
    Vertex operator *(double A){return Vertex(X*A,Y*A,Z*A);}
    Vertex operator -(Vertex A){return Vertex(X-A.X,Y-A.Y,Z-A.Z);}
    Vertex operator +(Vertex A){Vertex Res=*this;Res+=A;return Res;}
    double GetA(){return X/L();}
    double GetB(){return Y/L();}
    double GetC(){return Z/L();}
    bool Null(){if(X==0 && Y==0 && Z==0)return 1;return 0;}
    Vertex Normalize(){double l=Sqrt((X)*(X)+(Y)*(Y)+(Z)*(Z));X/=l;Y/=l;Z/=l;return *this;}
};