A previously unnoticed geometric pattern is present in the extremities of all tetrapods. Sets of straight and typically uninterrupted hinge lines pass through neighboring interphalangeal joints and across ungual tips. Four sets of these lines appear in basal polydactyl tetrapods, two medial sets, a transverse set and a lateral set. The two medial sets merge in primitive pentadactyl tetrapods. The resulting three line sets persist in later taxa, even when digits shrink and disappear. Primitively and typically the lines in each set are more or less parallel, but lines may converge, merge and shift as phalanges disappear or phalangeal proportions change. Confirming this geometric pattern, complex interphalangeal joint surfaces typically align with hinge lines and pad divisions parallel them. In addition, unguals rarely cross extensions of hinge lines and longer unguals may divert medially or laterally rather than cross them. Exceptions occur most commonly on ungual II. Line sets may exist because phalanges appear to flex and extend most efficiently in unison. Hinge line patterns appear to identify clades so they may, to a limited extent, be used taxonomically. Hinge lines also have predictive value in that missing phalanges, including unguals, can be reconstructed with confidence using hinge lines as size guides. Correct digit spread and metapodial configuration can also be determined in extinct taxa by seeking the appearance of continuous interphalangeal hinge lines in tested reconstructions.