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The threshold (32) for n = 1 has previously been given in [30, 37] and in [33, 38]. Thresholds (33) - (35) for n = 2 , 3 , 4 are new. The polynomial equation determining p$_{c}$ under the homogeneity assumption in Table VI for the 3-12 lattice has been given in I and [38], and $^{is 1}$− p + p 2 + p 3 − 7 p 4 + 4 p 5 = 0. 

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