<p>I don't know that we have a perfectly pure thread that would be considered canonical.  That's especially true for 3-way interactions.  You can sort the questions returned by <a href="https://stats.stackexchange.com/questions/tagged/interaction%2Binterpretation?tab=Frequent">searching</a> on <a href="https://stats.stackexchange.com/questions/tagged/interaction" class="post-tag" title="show questions tagged &#39;interaction&#39;" rel="tag">interaction</a> and <a href="https://stats.stackexchange.com/questions/tagged/interpretation" class="post-tag" title="show questions tagged &#39;interpretation&#39;" rel="tag">interpretation</a> by votes or frequency of linking to see if there's something you like.  Personally, I tend to link to <a href="https://stats.stackexchange.com/q/122246/7290">Interpretation of interaction term</a> in conjunction with <a href="https://stats.stackexchange.com/a/120035/7290">Interpretation of betas when there are multiple categorical variables</a>, but note that (a) these only pertain to a 2-way interaction, and (b) I wrote both of those answers.  Another of my answers I sometimes link to is the top portion of <a href="https://stats.stackexchange.com/a/49701/7290">Interaction in generalized linear model</a>.  Again, partly I'm more familiar with those because I wrote them.  Assuming someone actually goes to all three places and reads all of the answers, I think they could get a reasonable grasp of the idea, but then again, people may not do that and it wouldn't hurt to have all the information in a general form in one place.  So a canonical thread isn't a bad idea.  </p>

<p>I suspect that also trying to adequately cover 3-way interactions will be difficult and make the answer pretty long, though.  You'll also need to consider if you want to work through the distinction between categorical and continuous variables in an interaction.  </p>
