The elastic energy of a set of the twelve variants generated during the β -> α transformation of zirconium, with volume fractions f_i, i=1..12, is derived with simplifying assumptions and the conditions on the f_i to reach the energy minimum are established analytically. The minimum number of variants needed to reach this minimum is shown to be 6, and in this case, the variants have very specific volume fractions. Another result is that the maximum volume fraction of any variant is 1/3.