  A class of self-similar sets of entangled quantum states is introduced, for
which a recursive definition is provided. These sets, the "Bell gems," are
defined by the subsystem exchange symmetry characteristic of the Bell states.
Each Bell gem is shown to be an orthonormal basis of maximally entangled
elements. A non-trivial example Bell gem is presented. Quantum circuits for
producing the elements of this example from the computational basis states are
provided.
