Iota Alpha Pi
 

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I have a 1930 Baird's Manual. In 1930 there were 6 chapters, one of which was an alumnae group.

IAII was a historically Jewish sorority founded in 1903. The badge was diamond shaped with a red center. Upon the center was a skull & crossbones and the greek letters I A Pi. 24 pearls surround the red.

I don't know if they were ever a member of the NPC or not. All web references to the group are from members in Canada. I have a feeling that the Canadian chapters outlasted the US chapters. You can try writing a former member and get more info.

An online friend found this information in a later edition of Baird's:

I can update that a bit:
from the 1957 Baird's, page 79, where I A Pi is listed as an
"Associate Member" of NPC. In the 1963 Baird's, page 777, I A Pi is listed as an "active member" (not associate) -- number 29 out of 29 at that time.
Also, their badge DID change; your description is correct for their standard badge for many years, but when they associated with NPC, they added "two full-blown gold roses on each of the horizontal points."
Why this was done I'm not sure, but if I had to hazard a guess, I'd speculate that it was for the same reason D Phi E added the scroll at the bottom of their badge -- in D Phi E's case, to differentiate it more from SK or Tri Sigma, and in I A Pi's case to differentiate it from ADPi's diamond-shaped badge. (Yes, you would think the color of the enamel woul be enough, but hey.) At any rate, if you would like a photocopy of the info from the Baird's manuals I have referenced, let me know; I could mail or fax it -- I'd just need an address.
Best regards,
Drew Beisner