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Polygonal Complexes with Octahedral Links
Valle, Raciel

2011, Doctor of Philosophy, Ohio State University, Mathematics.

Octahedral complexes are polygonal complexes with octahedral graphs as links. In this paper we classify them with the aid of computer software.


More specifically, (2n,d)-octahedral complexes are 2-dimensional simply connected complexes admitting a flag transitive group of symmetries, such that each face is a d-gon, and such that each vertex link is the octahedral graph with 2n vertices.


For each d greater than or equal to 6, and each n we classify the (2n,d)-octahedral complexes in terms of properties of the group of symmetries of the octahedral graph.


With this result and some computer programs we give explicit descriptions of all (2n,d)-octahedral complexes for d greater than or equal to 6 and n less than or equal to 6.


We have partial results for d < 6. We classify (2n,3) complexes that are simplicial for all n. We give a conjectural description of all (2n,3) complexes in which simplices inject, and we give an example of a 1-vertex (14,3)-complex. We have some partial results concerning (2n,4)-complexes and we give some examples of (2n,5)-complexes.

Ian Leary, PhD (Advisor)
Michael Davis, PhD (Committee Member)
Ronald Solomon, PhD (Committee Member)
Alan Saalfeld, PhD (Other)
146 p.

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Valle, R. (2011). Polygonal Complexes with Octahedral Links. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Valle, Raciel. "Polygonal Complexes with Octahedral Links." Electronic Thesis or Dissertation. Ohio State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Valle, Raciel "Polygonal Complexes with Octahedral Links." Electronic Thesis or Dissertation. Ohio State University, 2011. https://etd.ohiolink.edu/

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