MathDB
Polyhedron

Source: HMMT 2008 Guts Problem 28

May 13, 2008
AMCAIMEgeometry3D geometryoctahedron

Problem Statement

Let P P be a polyhedron where every face is a regular polygon, and every edge has length 1 1. Each vertex of P P is incident to two regular hexagons and one square. Choose a vertex V V of the polyhedron. Find the volume of the set of all points contained in P P that are closer to V V than to any other vertex.
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