We all know the traditional Yin Yang symbol. Something like this.
I am lookng for a similar symbol that uses 3 characters instead of 2. Also, if this does exist, is there any meaning attached to it?
Korean symbol “Sam-Taegeuk”
http://www.san-shin.org/Sacred-Mtns-01.html
I remember it being prominent in the Seoul Olympics. Apparently the three colors stand for heaven, earth, and humanity.
There is such a symbol, exactly as you describe, including the dots as you see in the yin-yang symbol. It is used by the BDSM community:
There’s the triple spiral; land, sea, sky
That is disappointing. Nothing against the BDSM community, but I don’t necessarily want to be affiliated with them.
Perhaps you’d like a mitsu tomoe?
http://en.wikipedia.org/wiki/tomoe
There’s the roundel of the Irish Air Corps:
so don’t use their specific version then, its specifically black with the three dots, and is not well known anyway.
No one is likely to make a connection with any other colored variation, its far more likely that people will think it’s Korean.
Well, it’s pretty well known in the BDSM community. Wearing it could lead to some awkward conversations. 
This and this have three parts symmetrically located…but maybe not what you are after.
Apparenly Trefoil is the name for the category of symbol. Celtic knots may be worth investigating, as Scathach’s link suggests.
Ah, yes. I vote for this one too. It always reminded me of a shuriken that I used to own.