File:Polyhedron with no vertex visible from center (inside corner).png

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Description This simple, non-convex polyhedron is constructed so that none of its 24 vertices can be seen from a region around its center. This counterexample shows that placing observers at each vertex is not a solution to the 3-dimensional generalization of the art gallery problem. This image shows a view from the center of the polyhedron towards one of the corners. Observe that no vertices (marked with black balls) are visible: they're all hidden behind the yellow faces, just beyond the edge of the triangular gap through which the red face can be seen.
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Source Self-made using POV-Ray 3.6 for Windows.
Author Ilmari Karonen
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6 November 2007

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current04:03, 6 November 2007Thumbnail for version as of 04:03, 6 November 20071,280 × 1,024 (240 KB)Ilmari Karonen{{Information |Description=This simple, non-convex polyhedron is constructed so that none of its 12 vertices can be seen from a region around its center. This counterexample shows that placing observers at each vertex is not a solution t