DescriptionPolyhedron with no vertex visible from center.png
This simple, non-convex
polyhedron is constructed so that none of its 24 vertices, marked with black balls, 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. The blue faces are also not visible from the center. This polyhedron is topologically equivalent to the
rhombicuboctahedron.
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions
Outside view with the blue faces removed, showing the construction more clearly.
View from the inside facing one of the corners.
Panoramic 180 view from the inside.
Vector version with cross-section
POV-Ray source
This is the source code from which the image above is rendered. The permission given above applies to this source code as well.
{{Information |Description=This simple, non-convex
polyhedron is constructed so that none of its 12 vertices, marked with black balls, can be seen from a region around its center. This counterexample shows that placing observers at each
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
DescriptionPolyhedron with no vertex visible from center.png
This simple, non-convex
polyhedron is constructed so that none of its 24 vertices, marked with black balls, 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. The blue faces are also not visible from the center. This polyhedron is topologically equivalent to the
rhombicuboctahedron.
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions
Outside view with the blue faces removed, showing the construction more clearly.
View from the inside facing one of the corners.
Panoramic 180 view from the inside.
Vector version with cross-section
POV-Ray source
This is the source code from which the image above is rendered. The permission given above applies to this source code as well.
{{Information |Description=This simple, non-convex
polyhedron is constructed so that none of its 12 vertices, marked with black balls, can be seen from a region around its center. This counterexample shows that placing observers at each
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):