A polyhedron in Euclidean 3-space is called infinitesimally flexible if there exist tangent vectors of motions of the vertices that retain edge lengths, but change distances of at least one non-connected pair of vertices. In this paper, we describe a construction of such polyhedra inspired by examining models built from plastic triangles. We illustrate a method to construct polyhedra by gluing strips at their boundaries. Following the presented approach, we provide an example of a polyhedron that is indeed infinitesimally flexible.