theorem
  a,b,c,d are_coplanar implies a,b,d,c are_coplanar &
  a,c,b,d are_coplanar & a,c,d,b are_coplanar &
  a,d,c,b are_coplanar & a,d,b,c are_coplanar &
  b,a,c,d are_coplanar & b,a,d,c are_coplanar &
  b,c,a,d are_coplanar & b,c,d,a are_coplanar &
  b,d,a,c are_coplanar & b,d,c,a are_coplanar &
  c,a,b,d are_coplanar & c,a,d,b are_coplanar &
  c,b,a,d are_coplanar & c,b,d,a are_coplanar &
  d,a,b,c are_coplanar & d,a,c,b are_coplanar &
  d,b,a,c are_coplanar & d,b,c,a are_coplanar;
