A many-body Ising lattice model of monatomic systems is solved exactly on a new recursive lattice with the aim to study the metastability in supercooled liquids and the ideal glass transition. Interactions between particles farther away than the nearest neighbor distance are taken into consideration. The model has a strong antiferromagnetic interaction to give rise to an ordered phase identified as a crystal. Thermal properties including free energy, energy and entropy of the ideal glass and supercooled liquid state of the model are calculated. The computation results show both the first order melting transition and second order ideal glass transition (entropy crisis). The effects of different energy terms are studied. We also study the defects in the ideal glass, supercooled liquid and the crystal to support the theory that a glass can be treated as a highly defective crystal, since the ideal glass at absolute zero has much higher energy than the crystal.