Nathan,
You can do 
\char"10162
which just worked for me using Brill Roman.
You need to make sure the character is present in the font and in the right 
code point.
If there is a font which you are sure includes the character, but not in its 
Unicode position, 
you can also find out what its Glyph ID (GID) number is, and input it using 
\XeTeXglyph####

For example, using the same Brill Roman, you can get what you want using this:
\XeTeXglyph4979

Hope this helps.

J

> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sun, 8 Apr 2012 18:16:05 +0900
> From: Nathan Sidoli <[email protected]>
> To: Unicode-based TeX for Mac OS X and other platforms <[email protected]>
> Subject: [XeTeX] A special character
> Message-ID: <[email protected]>
> Content-Type: text/plain; charset="iso-8859-2"; Format="flowed"
> 
> Hello all,
> 
> I am trying to put a rare character into some text. It is the old Greek 
> 10, [10], which exists in most Greek fonts and in the one that I am 
> using (Gentium Plus).
> 
> http://kreativekorp.startlogic.com/charset/unicode.php?char=10162
> 
> The unicode point is U+10162.
> 
> When I copy-and-paste into my XeLaTeX document, and run it in the Greek 
> font I am using (I also tried a couple of others), I get no output.
> 
> Is there anyway that I can select the character I want from the unicode 
> point alone?
> 
> Thanks,
> 
> Nathan




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