The students in my physics class were playing with Rubik's Cubes this morning before class. This got us talking about solids. The traditional Rubik's Cube is a six-sided closed solid in a three dimensional space. Another student had a Rubik's Dodecahedron, which got us talking about the "simplest" possible Rubik's Solid. We decided that what we meant by simplest was "possessing the smallest number of sides". We settled on a tetrahedron (which apparently does exist in Rubik's form).
Then we got to talking about the simplest possible closed figure in spaces of varying dimension. It seems like the simplest possible closed figure composed of straight sides in a two dimensional space has three sides, a triangle. Similarly, the simplest possible closed figure composed of straight sides in a one dimensional space would be a line segment, with two sides (is this a stretch?).
Then class began.
Intuitively, it seems like the simplest possible closed figure whose sides are all straight in an $n$ dimensional space will have $n+1$ sides.
Is that intuition correct?
My formal training is in the Classics, so I'm not sure whether I've asked the question properly. What branch of mathematics thinks about questions like that, and is there a good introductory text for it?