Yeah, and this works for any "algebra" (ie. vector space with a way of multiplying vectors.) The three legged thing is what they call the "structure constants" for the algebra.
(a x b )(c x d) => ???
o o o o
\ / \ /
o - o => o
/ \ / \
o o o o
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