There is a nice paper on a similar topic by [Burger, Gritzmann and Klee "Polytope projection and projection polytopes"][1] .  They describe an algorithm to compute the minimum surface area projection of an n-dimensional simplex. Accord to the paper it is NP-hard to find the maximum surface area of a n dimensional simplex. 


  [1]: http://www.jstor.org/pss/2974444