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.

02. The four types of linear spaces based on the class n.a, for n ≤ 6. The fourth type is the enantiomorphic version of the third given above.

03. The single type of a linear space based on the class 2ñ.a, for n ≤ 3

04. The two types of linear spaces based on the class n:m.a, for n ≤ 6.

05. The four types of linear spaces based on the class n:2.a. The fourth type is the enantiomorphic version of the third given above.

06. The three types of linear spaces based on the class n.m.a, for n ≤ 6.

07. The two types of linear spaces based on the class 2ñ.m.a for n ≤ 3

08. The three types of linear spaces based on the class n.m:m.a

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.