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Jade Vinson : The Holyhedron Problem

Several years ago John Conway asked whether there could exist a polyhedron that "had a hole in every face," and coined the name "holyhedron" for them, if they should exist. We answer this question by constructing a holyhedron with 78,585,627 faces and genus 60,380,421. This is a polyhedron so that the interior of every face is connected but not simply connected.

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