The tetrahedron

(19)    {1,1,1} is a triangle with an edge length of three and {1,1,1,1} is a tetrahedron with an edge length of four, shown below.

KSubsets[l,k] gives all subsets of set l containing exactly k elements, ordered lexicographically

(20)    {-1,-1,-1,-1} is an upside down inside out (negative) tetrahedron, shown below, with an edge length of four (actually minus four: the sum of the four coordinates)..

Created by Wolfram Mathematica 6.0  (17 March 2008)