5 papers
Noncompact surfaces, triangulations and rigidity
Stephen C. Power
Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in R^3. In particular, e…
Partial triangulations of surfaces with girth constraints
Stephen C. Power
Barnette and Edelson have shown that there are finitely many minimal triangulations of a connected compact 2-manifold M. Similar finiteness results are obtained for cellular partia…
Parallelogram frameworks and flexible quasicrystals
S. C. Power
The first-order flex space of the bar-joint framework of a parallelogram tiling is determined in terms of an explicit free basis. Applications are given to braced paralle…
Isotopy classes of 3-periodic net embeddings
Igor Baburin, Stephen Power, Davide Proserpio
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. We obtain periodi…
Elementary proofs of Kempe universality
S. C. Power
An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage. Additionally it is…