Subject: shapes measures symmetry space
Who is asking: Student
I think you need to look at recent work on vision and cognitive science. One sourse I have found usefull is Donald Hoffman: Visual Intelligence - how we create what we see, Nortom 1998. In addition to nice illustrations and suggested 'rules' he makes the clear point that we are wired to see 3-D (and to interpret pictures which are ambiguous about the 3-D world, into certain consistent patterns for the 3-D situations). So 2-D is actually harder to explain - artificial, detached from early experience etc.! There are some neet visual illustrations at http://www.socsci.uci.edu/cogsci/personnel/hoffman/vi.html
Another book which MAY have a bit (or references to some sources) is the recent book of Lakoff and Nunez - Where Mathematics Comes From which is about the cognitative metaphors which permit the human brain to do mathematics at an unconscious (and therefore at conscious) level. Things like seeing a boundary curve, with an inside and an outside (key to parts of vision AND to basic logic like Venn Diagrams which you may have seen - but which are not just illustrations but root abilities for thinking).
It appears from recent work (The number sense - Dehaeme, or What Counts, Butterworth) that children are born with some wiring for small numbers (e.g. numbers 1, 2, 3 by a few days up to experiments at 2 months). It is likely that includes quite a bit about shape etc. So counting corners or edges or faces etc. should be something we are equiped to do early (well before school).
So I have given you some 'big references' which may not be easy to read. The experiments talked about there are pretty easy to follow. Some more of them are on the internet, linked from my course web page (see the bottom and near the top on that page) http://www.math.yorku.ca/Who/Faculty/Whiteley/Visual.menu.html