Would it make sense/work to do something like this ? (a x b )(c x d) => ??? o o o o \ / \ / o - o

Would it make sense/work to do something like this ? (a x b )(c x d) => ??? o o o o \ / \ / o - o => o / \ / \ o o o o Would the circle in the middle of the cross be a tensor of order 4 then? Edit: It's been a while since I did that but wouldn't that be the following in sum notation? eps_ijk a_j b_k eps_ilm c_l d_m = (new tensor)_jklm a_j b_k c_l d_m