I have an oddly specific reference request.
I keep encountering a class of problems where, loosely speaking, I have a geometric figure in $\mathbb{R}^n$ where each dimension is "supported" by a vertex of the figure. In other words, if I wanted to delete a vertex from the figure, I would simultaneously have to project my figure down a dimension.
All dimensions have a vertex, but not all vertices have a dimension. Thus, some vertices can be deleted "for free," but for every dimension there is some vertex whose presence is necessary and sufficient to keep that dimension in play.
I've encountered these figures in economics research (specifically, game theory) and in some computational linear algebra problems, but I haven't found a formal treatment of them in either.
Does this sound at all familiar to you? Do these figures have a name? Has anyone studied their properties?
Thanks in advance.