**UM Math Graduate Students Seminar**

Liz Jimenez

*University of Miami*

**will present**

**Enumerating faces of Zonohedra**

Friday, April 8, 2011, 2:30pm

Ungar Building Room 506

**Abstract:** A zonohedron is a 3-dimensional convex polytope defined as the Minkowski sum of line segments. A way to better understand zonohedra is to enumerate their faces and the incidences between the faces, in other words, to study their flag f-vector.

It has long been known that there is a duality between the nonempty faces of a zonohedron Z and the faces of the hyperplane arrangement whose fan is the same as the normal fan of Z. We define a family of 3-dimensional hyperplane arrangements and characterize the flag f-vectors of those arrangements. Then, we translate the results to the dual setting of zonohedra.

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