Abstract
One of the most important issues in the design processes of retractable plate structure is to determine the most suitable shape of the plates that form an enclosure without any gaps or overlaps in both closed and open configurations of the structure. One of the approaches to find the most suitable shape of the plates is based on mathematical tessellation technique without using any kinematical or numerical analyses. Due to the usage of RPS on many different areas in architecture, it is just as important to be able to iterate them regularly. This study both focuses on the iteration of planar RPSs that are formed based on 1-uniform tessellation and develops a relation between iteration capacity of RPS and plane symmetry groups. By the help of developed relationship, it tries to realize whether this structure can be derived from 1-uniform tessellation and which tessellation should be selected before obtaining it.
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