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 Dec 5 awarded Popular Question Oct 6 asked A singular value inequality Jan 16 awarded Supporter Dec 12 accepted Is there always a parallelogram cross-section of parallelepiped contained in the smallest box Nov 28 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? Nov 28 awarded Commentator Nov 28 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 Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box deleted 123 characters in body Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box added 28 characters in body Nov 28 awarded Cleanup Nov 28 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? Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box added 29 characters in body; added 2 characters in body Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box rolled back to a previous revision Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box added 127 characters in body Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box edited title Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box added 144 characters in body; edited title; added 4 characters in body; edited title; deleted 170 characters in body Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box edited title Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box added 16 characters in body Nov 28 comment Is there always a parallelogram cross-section of parallelepiped contained in the smallest box Dear Joe, thanks. I have revised it. Nov 28 revised Is there always a parallelogram cross-section of parallelepiped contained in the smallest box edited tags; deleted 149 characters in body