Your question caught my interest. Ran an eznec model for each.
Square - 71feet per leg at 50 feet elevation:
80M - Straight up, no nodes or directional bias. 8db gain, 0db gain at 20 degrees
20M - 4 nodes with 12db gain at 20 degrees with nodes on the axis (centre fed) or at the diagonal (corner fed)
Hexagonal - 49 feet per leg at 50 feet elevation
80M - Same as square - Straight up dropping to 0db gain at 20 degrees
20M - 6 nodes with 11dg gain off the end of the feed wire at 20 degrees. The other 4 nodes are 7db each.
If you have the space, you may want to expand the dimensions just a little bit and build a mega-loop. Google "Mega Loop" and you'll come up with several comparisons between it and conventional horizontal loops. Its basically a horizontal delta loop that is fed in one corner with a 4:1 balun. I've just been reading about them the past 2 days. I just wish I had enough space at my present QTH. Anyway, the articles on the web should provide some great reading material. Its lots of fun building wire antennas and it really doesn't cost much. Plus you get to tell everyone its home built!
I think you'd enjoy reading about them and maybe get a better understanding of how the different loop layouts affect radiation patterns. I found it pretty fascinating. Antenna design hasn't really changed much over the years. Actually the basics have been with us for a long long time. Almost every antenna out there is either a dipole, vertical or loop - some with multiple elements. Now that we have access to modeling software, folks are starting to change the configuration of these designs to see how it effects gain and radiation patterns. Occasionally someone comes up with results that can be used to an advantage in some installations. I think the mega-loop which is nothing more than a large
horizontal equilateral triangle loop fed at one corner is well worth investigating.
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