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{\bf Leah Wrenn Berman}
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{\bf Symmetric Simplicial Pseudoline Arrangements}
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A simplicial arrangement of pseudolines is a collection of topological
lines in the projective plane where each region that is formed is
triangular. This paper refines and develops David Eppstein's notion of
a kaleidoscope construction for symmetric pseudoline arrangements to
construct and analyze several infinite families of simplicial
pseudoline arrangements with high degrees of geometric symmetry. In
particular, all simplicial pseudoline arrangements with the symmetries
of a regular $k$-gon and three symmetry classes of pseudolines,
consisting of the mirrors of the $k$-gon and two other symmetry
classes, plus sometimes the line at infinity, are classified, and
other interesting families (with more symmetry classes of pseudolines)
are discussed.

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