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In Unicode, there are many characters named like "SQUARE APAATO" which look like this ㌀ - a number of katakana characters arranged in a square.

The full list is here: http://www.fileformat.info/info/unicode/block/cjk_compatibility/images.htm

Why do these characters exist, and how are they used? It feels like some of them are currency signs (doru, koruna) but I have no idea about the rest.

  • Most are currency and unit (SI and imperial unit). There are only a handful that are not. For the details, Wikipedia helpfully links to the Unicode block data file. – nhahtdh Aug 2 '16 at 9:09
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These are called 組文字, whose main purpose is to save space. Certain words such as アパート (="apartment building"), 株式会社 (="co. ltd.") appear in address books so often that publishing firms had special movable types with tiny fonts for them. Some common combinations were adopted in the JIS standard, on which Unicode was based.

組文字 might have been relatively common until 40 years ago or so, but recently this custom has become rarer. You don't usually have to use them yourself. But you may find some 組文字 for units (㌫, ㌕, etc) still in use in newspapers and magazines.

One similar example is 分注【ぶんちゅう】 or 割注【わりちゅう】, which is similar in purpose to "footnotes". You may find 割注 if you buy an old book published in 1960's or so. Recent good DTP software still support this.

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