We can just rotate our second diamond and compare it to the first diamond. Like this:
for(int i=0;i<4;i++)
{for(int j=0;j<3;j++)
{if(a==b)
{cout<<"equal"<<endl;return 0;}
// Rotate diamond around current base-face
string x=e+b[2]+b[3]+b[1];
b=b[0]+x;}
string t="abcd";
// Change base-face
if(i!=2)
{t[0]=b[1];t[1]=b[3];
t[2]=b[2];t[3]=b[0];}
else
{t[0]=b[2];t[1]=b[1];
t[2]=b[3];t[3]=b[0];}
b=t;}