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Polygonal Complexes with Octahedral Links

Valle, Raciel

Abstract Details

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.

Recommended Citations

Citations

  • Valle, R. (2011). Polygonal Complexes with Octahedral Links [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306345474

    APA Style (7th edition)

  • Valle, Raciel. Polygonal Complexes with Octahedral Links. 2011. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1306345474.

    MLA Style (8th edition)

  • Valle, Raciel. "Polygonal Complexes with Octahedral Links." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306345474

    Chicago Manual of Style (17th edition)