  The Calabi-Yau spaces with SU(m) holonomy can be studied by the algebraic way
through the integer lattice where one can construct the Newton reflexive
polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be
directly related with the $n$-ary algebras. To find such algebras we study the
n-ary generalization of the well-known binary norm division algebras, ${\mathbb
R}$, ${\mathbb C}$, ${\mathbb H}$, ${\mathbb O}$, which helped to discover the
most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the
most important example, we consider the case $n=3$, which gives the ternary
generalization of quaternions and octonions, $3^p$, $p=2,3$, respectively. The
ternary generalization of quaternions is directly related to the new ternary
algebra and group which are related to the natural extensions of the binary
$su(3)$ algebra and SU(3) group. Using this ternary algebra we found the
solution for the Berger graph: a tetrahedron.
