Turning Orthogonally Convex Polyhedra into Orthoballs
نویسندگان
چکیده
As a step towards characterizing the graphs of orthogonally convex polyhedra, we show that for any simple orthogonally convex polyhedron there is an orthoball that is equivalent in the sense that it has the same graph and the same face normals. An orthoball is a simple orthogonally convex polyhedron with a point inside that sees the whole interior (informally, it is “round”). The consequence for reconstructing polyhedra from graphs is that if we start from a 3-regular planar graph labelled with face normals, and wish to find a corresponding orthogonally convex polyhedron, then we can restrict our search to orthoballs.
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