28

Part of 2008 Harvard-MIT Mathematics Tournament

Problems(1)

Source: HMMT 2008 Guts Problem 28

P

be a polyhedron where every face is a regular polygon, and every edge has length

1

. Each vertex of

P

is incident to two regular hexagons and one square. Choose a vertex

V

of the polyhedron. Find the volume of the set of all points contained in

P

that are closer to

V

than to any other vertex.

AMCAIMEgeometry3D geometryoctahedron