  We show that the low-energy sector of the S=1/2, antiferromagnetic Heisenberg
model on a one-dimensional lattice of coupled tetrahedra consists of 2^N
replica of the spectrum of the dimerized Heisenberg chain, where N is the
number of tetrahedra.
  This provides a proof of the following properties: i) there is a residual
ground-state entropy per spin equal to 2^{1/4}; ii) there is a singlet-triplet
gap as long as the coupling between the tetrahedra is smaller than the internal
one. These properties are compared to available results on the pyrochlore
lattice.
