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Wikipedia says that

The IBM 1620 Model I used the Cyrillic character Ж (pronounced zh) on the typewriter as a general purpose invalid character with correct parity.

The Model II used a new character ❚ (called "pillow") as a general purpose invalid character with correct parity.

(The character ❚ is rendered as U+275A HEAVY VERTICAL BAR).

References, or scans of printouts with either character, are not provided on the wiki page; assuming that's true about the letter Ж on Model I, how come an arbitrary character from another script was chosen? Is there a story behind it?

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Sorry to debunk that myth. All information I'm aware of looks like it isn't a Zhe, but a made up symbol. Several sources, including IBM manuals do show quite different shapes.

Sources pro Zhe:

A) IBM 1620 CPU Model 1 Manual

by IBM (found here) features a glyph much like a Zhe:

enter image description here

Sources contrary Zhe:

B) IBM 1620 Input Output Units Manual

by IBM (found here) shows on page 22 something that can be described as two semi circles back to backwith a horizontal bar, much like a strike thru:

enter image description here

C) Reference Manual IBM 1620 Data Processing System

revision July 1961 by IBM (found here) prints on page 36 quite the same symbol, this time rotated by 90 degree:

enter image description here

D) IBM 1620 Parts Catalog

form May 1963 by IBM (found here) identifies the typebar for that symbol as #7 and associates this with the same symbol as the reference manual.

enter image description here

E) BASIC PROGRAMMING CONCEPTS AND THE IBM 1620 COMPUTER

by Daniel Leesons shows at page 279 an image, again like two semi circles, but this time attached to either side of a quite long vetical bar:

enter image description here

A bit confusing that four genuine IBM 1620 manuals of the same time show three different glyphs, while another book of the same time frame shows another different one. And only one of them might be seen as Zhe.

So far, and despite the similarity, I'm pretty sure that this symbol is not the Cyrillic letter Zhe, but a made up one. Much like the many other the 1620 typewriter features.

I guess people just tried to find a name like with other 'weired' chars like dagger, doubble dagger, pillow, lozenge, box, diamond, delta, ruber, and so on. Here maybe someone with basic Russian might have brought up the idea and it stuck. Or the Wiki remark is just one of the usual retroactive made up explanations, not rare at all among wiki entries. As for myself, I never heared about that theory, but then again, I never realy worked on a 1620 either.

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    I've expected that much because a true Ж wouldn't make sense. A link to the book or to the picture of the character, if you intended to add one, is missing, though.
    – Leo B.
    Sep 26 '17 at 2:08
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    @Jules Nice find (I assume you refer to page 52, there is none on 56). Now, takeing a look at page 22 in the IBM 1620 Input Output Units Manual (same archive) where the Typewriter is described, a different symbol is shown. It's also based on two semi circles, but features a horizontal bar, exactly like the strike thru that is used to mark a parrity error, which would make sense. Now, on page 36 of the Jul61 Reference Manual (same archive), there is a similar symbol shown, but this time rotated by 90 degree. Your guess is as good as mine. I'd still go with a made up symbol, not a Zhe.
    – Raffzahn
    Sep 26 '17 at 8:34
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    I disagree with this "debunking". I asked the Computer History Museum's 1620 restoration team, and they said the Model I printed a Cyrillic Ж for unknown characters, but slightly narrower so it matched the width of other typewritten characters. The Ж character was part of the 1620 console typewriter's typebars. It was not made by strikethrough; the only overprinting the typewriter could do was an overscore flag mark, and a center-hyphen for parity errors.
    – Ken Shirriff
    Sep 27 '17 at 22:55
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    @KenShirriff Beside hearsay, wouldn't it be great to ask them to just pull in a clean sheet of paper and have a clear print to show how it looks?
    – Raffzahn
    Sep 28 '17 at 0:10
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    @KenShirriff The typewriter can be operated localy. And if you're not sure how to do that, just put in a sheet, and move the bar in question by hand. As it's free flying, this can be done without harming the mechanics. And last, if afraid to try this, remove the cover, clean the typebar with some alcohol and take a few high res pictures of the typehead. Either way, we can solve it - and until then, you might want to check the manual linked in the now rewriten answer.
    – Raffzahn
    Sep 28 '17 at 1:09

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