Smallest magic squares of triangular numbers (and of polygonal numbers)

In 1941, Royal Vale Heath proposed this short problem E 496 in The American Mathematical Monthly:

With only the proof of n £ 8, this problem remained unsolved. "Better late than never", here is the solution found in April 2007... 66 years later:

My solution was published in the October 2007 issue of The American Mathematical Monthly, including this example:

On this subject, read also the Mathematical Tourist article written in November 2007 by Ivars Peterson:

My solution was also published in the January 2008 issues of Pour La Science (page 31) and Sciences et Avenir  (page 20).

A more detailed text than the version published in the Monthly is available in two formats:

In this expanded solution, you will see:

Smallest magic squares of hexagonal to decagonal numbers

Charles W. Trigg published in School Science and Mathematics and in the Journal of Recreational Mathematics his magic squares of order 8 of hexagonal to decagonal numbers, see references.
But it is possible to construct smaller magic squares. In the extended solution seen above, my magic squares of ordre 7 of hexagonal to decagonal numbers were announced but not given, because "it might be boring to give all my samples". After questions from some readers of this website, here are revealed my squares of order 7, the smallest possible order for squares of consecutive hexagonal to decagonal numbers.

In January 2013, Lee Morgenstern constructed these magic squares of order 4, the smallest known order for squares of distinct hexagonal and heptagonal numbers. Squares of order 4 of octogonal to decagonal numbers are unknown.

And in November 2014, he added these squares of octagonal, nonagonal and decagonal numbers:

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