View a plane tree drawn in $\mathbb{R}^2$ as a joining of geometric (straight) segments at endpoints such that (a) they avoid intersecting one another (except where they share a vertex), and (b) they avoid creating a cycle, which would enclose a positive planar area. I am interested in the generalization to $\mathbb{R}^3$ as follows. Join together (flat) polygons, glued edge-to-edge, such that (a) they avoid intersecting one another (except where they share vertices and/or edges), and (b) they avoid enclosing (water-tightly) a positive volume.

My question is:

Is there a name for this construct? Has it been studied?

I am mainly seeking references to any literature on this or related concepts.
Of course there is a generalization to $\mathbb{R}^d$, but I would be happy to learn
of work just generalizing *plane trees* to *???* in $\mathbb{R}^3$.
I cannot think of what it might be named: *open panel structures*?
It's come up in my work, and I would be delighted to christen it, but surely it has been
studied...?

Thanks in advance!

**Addendum.** As Greg Kuperberg kindly explained, the concept I described is
a collapsible complex. It is usually defined for simplicial complexes, but works
as well when the constituents are polytopes rather than simplices, e.g., polygons in $\mathbb{R}^3$.