Cubic Partial Cubes from Simplicial Arrangements, now online at arxiv.org, describes in more detail the connections I outlined here between the two subjects in the title. While writing it, I discovered a partial explanation for the fact that sometimes gluing together parts of two arrangements gives another partial cube, and sometimes it doesn't: you get a partial cube whenever the zonotopal tilings dual to the two arrangements can be overlaid on top of each other to get a finer zonotopal tiling. I'm not entirely sure what to do with the paper; the logical target is EuJC, but it's an Elsevier journal and for various reasons I'm not entirely happy with that company lately. Another discrete math journal, maybe?
I also updated my pub list to include Really Straight Drawings I: Planar Graphs, a journal submission with Dujmović, Suderman, and Wood based on part of a previous conference paper by the other three authors and including also some older but heretofore unpublished results of mine on dilation of planar graphs.
I'm not sure that the business activities of a distantly-related company under the same corporate banner should affect your choice of publishing outlet one way or another. If the readers of EuJC are the best audience for this work, send it there. If they aren't - don't.
Actually, while colorful, that isn't the biggest reason I'm unhappy with Elsevier — it's more about the way they and similar corporate-controlled journals lock in researchers through precisely this mechanism (theirs is the go-to journal for some subfield) and then demand large fractions of university library budgets as ransom for access to their research. Access that, these days, isn't even permanent — it used to be that when a library bought a journal it stayed bought, and if a journal gradually became irrelevant you could safely cancel it, but no more. You can't cancel any more because then you'd lose your electronic access to all the back issues, and also because the publishers require you to buy big bundles of all their journals rather than ordering a la carte.