  We classify the ultrahomogeneous complete 3-edge-coloured graphs (3-graphs)
with simple theory. This extends Lachlan's result (a corollary of the Effective
Classification Theorem for stable structures) classifying the stable
homogeneous 3-graphs.
  The unstable structures in this class are:
  + Primitive structures: The random 3-graph $\Gamma^{i,j,k}$
  + Imprimitive structures with infinite classes:
  * $K_m^i[\Gamma^{j,k}]$, $m\in\omega+1$
  * $\Gamma^{i,j}[K_\omega^k]$
  * $\mathcal B_n^{i,j}$, $n\in\omega$, $n\geq2$
  * $\mathcal B^i$
  + Imprimitive structures with finite classes:
  * $C^i(\Gamma^{j,k})$
  * $\Gamma^{i,j}[K_n^k]$, $n\in\omega$
  Where $\{i,j,k\}=\{R,S,T\}$, $\mathcal B_n^{i,j}$ is the random $n$-partite
graph, and $\mathcal B$ is the Fra\"iss\'e limit of the class of all finite
3-graphs in which the predicate $i$ is an equivalence relation (i.e., the
triangles $iij$ and $iik$ are forbidden). Finally, $C^i(\Gamma^{j,k})$ is the
3-graph obtained from the following construction: enumerate the Random Graph in
predicates $j,k$ as $\{v_n:n\in\omega\}$. For each vertex $v_n$, there are two
vertices, $a_n$ and $b_n$ in $C^i(\Gamma^{j,k})$ which are $i$-related. There
are no more $i$-edges, and if $j(v_n,v_m)$ holds, declare $j(a_n,a_m)\wedge
j(b_n,b_m)$. All other edges are of type $k$.
