1957 Topps 4th Series Double Prints?

[metroac]

I recently started to build a 1957 Topps set and I'm confused about the supposedly scarce 4th Series. I found a couple of online checklists that show 21 cards from that series as having been double printed. I've looked for photos of uncut sheets, and I've seen sheets of 55, 110 and 121 cards, which I think must have started out as 132 card sheets of 12 rows of 11 cards.

However, the only sheets I've seen are of the 1st Series, and they include Williams #1, Mantle #95, and the League Presidents #100. I haven't seen any 4th or 5th Series sheets. Although Topps designated the first four Series as containing 88 cards each, it's clear from photos of the 1st Series sheets that the printing sheets don't match up with the "series" as listed on the checklist cards.

Does anyone know whether the 21 cards in the tough 4th Series were really double printed? Were there really 22? Were the rows duplicated? Were they added as filler to the 5th Series (which only has 55 cards)?. 55 cards is 5 rows of 11, which dovetails with the 110 card, 10 row sheets, so the 5th Series could be printed twice on a sheet of 110. If Topps printed in 132 card sheets, the 5th Series might have two sets of 55 (that is, cards 353-407) plus 22 (two horizontal rows) 4th Series double prints?

Does anyone know? Any speculations?