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On Sat, 1 Feb 2003, Roozbeh Pournader wrote:

    [...]

    (AMS has also got something called LOW ASTERSIK encoded in Unicode 3.2,
    but I really don't know about the usage, as I could not find much
    information about it in the original proposal. But the glyph used for that
    in the charts appears too lower than a math asterisk. Barbara?)

the "low asterisk" has unicode value 204E; it is a regular-sized
asterisk in approximately subscript position.

there were two sources for this:
 - the sgml public entity sets; this is in the isotech set, "lowast"
 - the american physical society (aps) included it in their collection
   that became a part of the "math" submission to unicode

this asterisk is not in the proper position to be used for a bullet;
the only centered asterisk is at unicode 2217 (already noted), in the
math area.  but this doesn't necessarily preclude it from being used
in a non-math context -- the unicode technical committee is very
hesitant to add additional characters for which the shape is identical
to something that's already present.  there was no non-math centered
asterisk included in the collection of symbols submitted for the
stix effort.
                                                        -- bb