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Dec
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awarded  Popular Question
Oct
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asked A singular value inequality
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awarded  Supporter
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accepted Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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comment Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
I plotted $A(Q)$ for A={{34, 33, 33}, {33, 34, 33}, {33, 33, 34}} by using Mathematica and got an object more than 6 faces, which is strange to me. Did you plot $A(Q)$ of your example?
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awarded  Commentator
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comment Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
For "parallelepiped", you can go to en.wikipedia.org/wiki/Parallelepiped
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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awarded  Cleanup
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comment Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
Dear Sergei, your example is very interesting. If you plot the image of $Q$ under $A$, $A(Q)$ is not a parallelepiped, as it has more than 6 faces. The question should be: If $A(Q)$ is a parallelepiped, is there always one of the planes $P_0$ such that the plane does not intersect with the interior of any two adjacent edges?
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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comment Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
Dear Joe, thanks. I have revised it.
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revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box
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