Ken's Puzzle of the Week

Magic Pyramid

         A
        /|\
       / | \
      /  e  \
     /   |   \
    h    |    i
   /    -D-    \
  /  f--   --g  \
 / --         -- \
B--------j--------C
  

Place ten numbers at the four corners and six connecting edges of a tetrahedron, such that either:

  1. Each edge (corner-middle-corner) has the same sum, or
  2. Each face (three corners and middles) has the same sum.
In each case, all numbers are unique.  Minimize the largest number and the common sum.  For comparison of solutions, let A>B>C>D.

Source: Original.

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