  A parametrization of integral Descartes configurations (and effectively
Apollonian disk packings) by pairs of two-dimensional integral vectors is
presented. The vectors, called here tangency spinors defined for pairs of
tangent disks, are spinors associated to the Clifford algebra for
three-dimensional Minkowski space. A version with Pauli spinors is given. The
construction provides a novel interpretation to the known Diophantine equation
parametrizing integral Apollonian packings.
