In analogy to flexible quadrilateral bipyramids, also known as Bricard octahedra, we study flexible couplings of two Bennett 4R mechanisms. The resulting bi-Bennett structures can be used as building blocks of flexible tubes with quadrilateral cross-section that possess skew faces. We present three 4-dimensional families of flexibly arranged Bennett tubes and discuss some of their properties as well as their relation to flexible bipyramids and biprisms, respectively. As a by-product, we also obtain a novel class of mobile 6R loops. • In analogy to flexible bipyramids we study flexible couplings of two Bennett 4R loops. • These bi-Bennett can be used as building blocks of flexible tubes with skew faces. • Three 4-dim families of bi-Bennetts are presented and their properties are discussed. • As a by-product, we also obtain a novel class of mobile 6R loops.
Georg Nawratil (2026) studied this question.