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We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping " volcano unfolding. " These un-foldings keep the base intact, unfold the sides outward, splayed around the base, and attach the top to the tip of some side rib. Our result… (More)

- Patricia Cahn
- 2013

Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on a surface. Turaev conjectured that his cobracket ∆(α) is zero if and only if α is a power of a simple class. Chas constructed examples that show Turaev's conjecture is, unfortunately, false. We define an operation µ in the spirit of… (More)

- Melanie Albert, Jenna Bratz, Patricia Cahn, Timothy Fargus, Nicholas Haber, Elizabeth Mcmahon +2 others
- 2008

Given a group G with generators ∆, it is well-known that the set of color-preserving automorphisms of the Cayley color digraph Γ = Cay ∆ (G) is isomorphic to G. Many people have studied the question of when the full automorphism group of the Cayley digraph is isomorphic to G. This paper explores what happens when the full automorphism group of G is not… (More)

We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping " volcano unfolding. " These un-foldings keep the base intact, unfold the sides outward, splayed around the base, and attach the top to the tip of some side rib. Our result… (More)

- Nadia Benbernou, Patricia Cahn, Joseph O 'rourke

We define a notion for unfolding smooth, ruled surfaces , and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping " volcano unfolding. " These un-foldings keep the base intact, unfold the sides outward, splayed around the base, and attach the top to the tip of some side rib. Our result… (More)

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