Shape Computation Lab

Rod Symmetry

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01. Instances of the the four n-fold point groups, for n=4, from which the seven symmorphic groups are derived.

Athanassios Economou

2006

Keywords: Shape studies; Symmetry; Linear Growth; Symmorphic groups

The project looks closely at a specific class of three-dimensional designs that have one axis of growth and presents all possible algebraic structures that capture the symmetries of these designs. A specific set of seven types of designs is discussed, the symmorphic designs, and is used as a framework to derive the non-symmorphic designs and to complete all three-dimensional linear structures. The complete catalogue of all nineteen space structures that may be generated in this manner is presented for n-fold screw rotations, n <=6.