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Re: lozenge

Hans Aberg speculates about the lozenge character:

>> The \lozenge looks as though it is not as all designed for that useage or
>> purpose, and I can not immediately recall any particular mathematical
>> useage. 

The lozenge goes back a long way on computers: it was a standard character
in the 6-bit BCD character set on IBM mainframes in the 1950s: see
Chapter 2 of

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

  author =       "Charles E. Mackenzie",
  title =        "Coded Character Sets: History and Development",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xxi + 513",
  year =         "1980",
  ISBN =         "0-201-14460-3",
  LCCN =         "QA268 .M27 1980",
  price =        "US\$24.95",
  series =       "The Systems Programming Series",
  bibdate =      "Wed Dec 15 10:38:43 1993",

It was BCD character octal 063, the same as right parenthesis (4 other
character pairs were also mapped to a common position, see Fig 2.21
on p. 38).  

The lozenge appears to have been dropped in EBCDIC, and is absent
in ASCII.  I do recall seeing it on IBM punched cards and on
IBM printer chains in the 1960s.  Unicode has character 2311 hex
with the name "square lozenge", a graphic resembling that of the
BCD character, but it also has character 25ca hex with the name
"lozenge", with a graphic that is barely distinguishable from
character 25c7 "white diamond".  

My Webster's New Twentieth Century Dictionary has the definition
	1. a figure with four equal sides, having two acute and
	two obtuse angles; a rhomb; a diamond

It appears the Unicode has followed the dictionary definition
in naming 25ca, even though the BCD graphic was always oriented
like a square is conventionally displayed, but with inward-rounded
sides.  Neither the Chicago Manual of Style, nor Words into Type,
nor the MLA Handbook, mention the lozenge in their indexes.

The Adobe Symbol encoding has lozenge at 224 dec (340 octal), and the
PostScript Language Reference Manual, 2nd edition, displays it as a
narrow white diamond.  I found lozenge in a few other Adobe fonts, but
only as an unencoded character.  It is present in only 2 of the 500
Bitstream fonts (SymbolProportionalBT-Regular and
NewspaperPiBT-Regular), and its shape there is also a white diamond.

Nelson H. F. Beebe                  Tel: +1 801 581 5254
Center for Scientific Computing     FAX: +1 801 581 4148
Department of Mathematics, 105 JWB  Internet: beebe@math.utah.edu
University of Utah                  URL: http://www.math.utah.edu/~beebe
Salt Lake City, UT 84112, USA