  Materials science has adopted the term of auxetic behavior for structural
deformations where stretching in some direction entails lateral widening,
rather than lateral shrinking. Most studies, in the last three decades, have
explored repetitive or cellular structures and used the notion of negative
Poisson's ratio as the hallmark of auxetic behavior. However, no general
auxetic principle has been established from this perspective. In the present
paper, we show that a purely geometric approach to periodic auxetics is apt to
identify essential characteristics of frameworks with auxetic deformations and
can generate a systematic and endless series of periodic auxetic designs. The
critical features refer to convexity properties expressed through families of
homothetic ellipsoids.
