  This paper proposes a new mathematical approach to characterize native
protein structures based on the discrete differential geometry of tetrahedron
tiles. In the approach, local structure of proteins is classified into finite
types according to shape. And one would obtain a number sequence representation
of protein structures automatically. As a result, it would become possible to
quantify structural preference of amino-acids objectively. And one could use
the wide variety of sequence alignment programs to study protein structures
since the number sequence has no internal structure.
  The programs and this paper with clear figures are available from
http://www.genocript.com.
