  We introduce and study the higher tetrahedral algebras, an exotic family of
finite-dimensional tame symmetric algebras over an algebraically closed field.
The Gabriel quiver of such an algebra is the triangulation quiver associated to
the coherent orientation of the tetrahedron. Surprisingly, these algebras
occurred in the classification of all algebras of generalised quaternion type,
but are not weighted surface algebras. We prove that a higher tetrahedral
algebra is periodic if and only if it is non-singular.
