Matlab coordinates and edge lengths supporting "Flexible polyhedra", "Optimising the Steffen flexible polyhedron" and "Flexible polyhedra with two-mechanisms"

These data Matlab files. They are generated from running Matlab programmes. The file types are various Matlab file types for running different functions of Matlab coding. These data are generated by Iila Lijingjiao during her PhD studies at Cambridge University in 2013-2015. These data are for calculating and viewing various flexible polyhedra in her PhD research topic "Optimising flexible polyhedra". These files and data from Matlab coding are for maximising the range of movement in existing polyhedra that bend about theirselves, and for devising polyhedra with more than one degree of freedom. The two types of flexible polyhedra that are optimised are the Steffen flexible polyhedron and another flexible polyhedron devised by Tomohiro Tachi, who is the co-author of three papers these data are supporting. These data contain the edge lengths and the coordinates of vertices of both types of the flexible polyhedra described above. The edge lengths and the coordinates of vertices are of the original, changed and optimised polyhedra. The majority of the files are raw data. Processed data, which is the range of bending movement against the regularity of the shape of polyhedra, are also presented. Instructions regarding how to use the Matlab codes in order to use the data - coordinates of vertices - stored in the Matlab data files are given in sub files

Flexible polyhedra with two degrees of freedom

Proceedings of the International Association for Shell and Spatial Structure

Optimizing the Steffen flexible polyhedron

We revisit Steffen’s known flexible polyhedron, originally described in 1978, and investigate whether we can increase its range of motion by varying his original dimensions. We also define the regularity of a polyhedron. Using a simulated annealing algorithm, we perform multi-objective optimization on the Steffen polyhedron to achieve both maximum regularity and range of motion. The results show that we are able to both increase the range of motion possible for the polyhedron, while still making the polyhedron more regular