Summary: Buildup of internal self-stresses in hyperstatic adaptive structures resists actuation. A recent paper by S. D. Guest and J. W. Hutchinson [ibid. 51, No. 3, 383–391 (2003; Zbl 1100.74593)] shows that periodic infinite truss structures cannot be both statically and kinematically determinate structures; therefore, a rigid infinite lattice bar framework must be hyperstatic. This paper shows that it is possible to design adaptive periodic infinite truss structures that can achieve any state of uniform strain without energy cost by actuating only a subset of the bars in a coordinated fashion. We show that actuation of only 3 bars in two dimensions or 6 bars in three dimensions per unit cell is required. A mathematical apparatus is developed and an example of such a bitriangular lattice structure is given, along with accompanying illustrations. Supporting animations can be found at the authors’ website.