= Solution
The beta phase has a <primitive cubic lattice> with an eight-atom <atomic basis of a crystal>, rather than a <body-centred cubic lattice>. A <lattice translation> must map the entire atomic arrangement onto itself. For example, the putative body-centering vector $(1/2,1/2,1/2)$ maps $(1/4,1/2,0)$ to $(3/4,0,1/2)$ modulo integer coordinates, where the given <atomic basis of a crystal> has no atom. None of the seven nonzero basis positions generates a translation that preserves all eight sites. Therefore
$$
\boxed{\text{Bravais lattice: primitive cubic; basis: eight atoms.}}
$$
The presence of atoms at both the origin and the body centre alone is insufficient to establish body-centering of the full <crystal structure>.
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