A Polyhedron Full of Surprises

SummaryThe problem of geometric realization for convex polyhedra, which satisfy certain desirable properties, has received quite a bit of attention lately. Interest, mainly, has been on polyhedral representations where either all of the vertex coordinates are small integers, or all of the edge lengths are integers, or all of the edges are tangent to a sphere. In general, it is not easy to construct a convex polyhedron satisfying any of those criteria. We introduce a remarkable polyhedron that satisfies all of them.