Dilational Triangulated Shells Using Pantographs

Dilational structures are one degree of freedom structures able to change their size without changing their global shape. In this paper, we present a method to create dilational shells with arbitrary curvature. For this, we designed triangular tiles, which can be placed on a triangulation of the desired surface. We present the method and illustrate it with the example of a dilational octahedron. Using this regular polygon, we demonstrate that the whole structure has a single degree of freedom, and that the maximum obtainable scaling factor is directly linked to the range of motion of the individual triangular tiles.