Editing Perfect magic cube (section)

{{Short description|Magic cube with extra constraints}}
{{Use dmy dates|date=September 2023}}
{{original research|date=November 2016}}

In [[mathematics]], a '''perfect magic cube''' is a [[magic cube]] in which not only the columns, rows, pillars, and main [[space diagonal]]s, but also the [[cross section (geometry)|cross section]] diagonals sum up to the cube's [[magic constant]].<ref>{{Cite web|url=http://mathworld.wolfram.com/PerfectMagicCube.html|title=Perfect Magic Cube|last=W.|first=Weisstein, Eric|website=mathworld.wolfram.com|language=en|access-date=2016-12-04}}</ref><ref>{{Cite web|url=http://www.fq.math.ca/Scanned/19-2/alspach.pdf|title=Perfect Magic Cubes of Order 4m|last1=Alspach|first1=Brian|author1-link=Brian Alspach|last2=Heinrich|first2=Katherine|author2-link= Katherine Heinrich |date=|website=|publisher=|access-date=December 3, 2016}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=D_XKBQAAQBAJ&q=perfect+magic+cube&pg=PA2203|title=CRC Concise Encyclopedia of Mathematics, Second Edition|last=Weisstein|first=Eric W.|date=2002-12-12|publisher=CRC Press|isbn=9781420035223|language=en}}</ref>

Perfect magic cubes of order one are trivial; cubes of orders two to four can be [[mathematical proof|proven]] not to exist,<ref>{{Cite book|url=https://books.google.com/books?id=-mu8O8RMG6QC&q=perfect+magic+cube&pg=PA101|title=The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions|last=Pickover|first=Clifford A.|date=2011-11-28|publisher=Princeton University Press|isbn=978-1400841516|language=en}}</ref> and cubes of orders five and six were first discovered by [[Walter Trump]] and [[Christian Boyer]] on November 13 and September 1, 2003, respectively.<ref>{{Cite web|url=http://www.trump.de/magic-squares/magic-cubes/cubes-1.html|title=Perfect Magic Cubes|website=www.trump.de|access-date=2016-12-04}}</ref> A perfect magic cube of order seven was given by [[A. H. Frost]] in 1866, and on March 11, 1875, an article was published in the [[Cincinnati Commercial]] newspaper on the discovery of a perfect magic cube of order 8 by [[Gustavus Frankenstein]]. Perfect magic cubes of orders nine and eleven have also been constructed.
The first perfect cube of order 10 was constructed in 1988 (Li Wen, China).<ref name=":1" />