  We continue the study of Exceptional Periodicity and Magic Star algebras,
which provide non-Lie, countably infinite chains of finite dimensional
generalizations of exceptional Lie algebras. We analyze the graded algebraic
structures arising in the Magic Star projection, as well as the Hermitian part
of rank-3 Vinberg's matrix algebras (which we dub HT-algebras), occurring on
each vertex of the Magic Star.
