Based on the triangular lattice and its depletions there are three simple f
rustrated antiferromagnetic Heisenberg models in two dimensions. The first
two, the triangular and kagome lattices, have been examined in the recent p
ast. The triangular lattice seems to have a long range order whereas the ka
gome does not show the long range order. But these results are still contro
versial. This work is concentrated on a third type of this lattice family i
n order to improve the understanding of the connection between the long ran
ge order and coordination number in low dimensional systems. Bets has descr
ibed the geometric properties of this lattice. It has a coordination number
5, which lies precisely between coordination numbers 6 and 4 of the other
two lattices. The low-lying spectra and the correlation functions of finite
lattices have been examined to discuss the possibility of a long range ord
ered ground state in the 1/7-depleted triangular lattice. The low-lying spe
ctrum is generated by an exact diagonalization, and the tower of states beh
avior points to a long range ordered ground state.