When one is gay and Jewish.
Shape was chosen by analogy with the common triangular road hazard signs in Germany that denote warnings to motorists. Here, a triangle is called inverted because its base is up while one of its angles points down.
The most common forms of the badge were:
Red triangle — political prisoners (social democrats, trade unionists, liberals, communists, Freemasons, anarchists.) Some anarchists, and other "enemies of the state," were also given a black triangle.
Green triangle — "habitual criminals" (ofttimes Kapos).
Blue triangle — foreign forced laborers, emigrants.
Pink triangle — homosexuals and sexual offenders.<2>
Purple triangle — Jehovah's Witnesses.
Black triangle — people who were deemed "asocial elements," including
Roma (Gypsies), who were later assigned a brown triangle
The mentally retarded
The mentally ill
Alcoholics
Vagrants and beggars
Aristocrats
Intellectuals
Pacifists
Conscription resisters
The habitually "work-shy"
Prostitutes<3><4>
Some anarchists.
Brown triangle — Roma (Gypsies) (previously wore the black triangle).<5>
Double-triangle badges resembled two superimposed triangles forming a Star of David.
Two superimposed yellow triangles — a Jew.
Red inverted triangle superimposed upon a yellow one — a Jewish political prisoner.
Green inverted triangle upon a yellow one — a Jewish "habitual criminal".
Purple inverted triangle superimposed upon a yellow one — a religious dissident of Jewish descent.<6>
Pink inverted triangle superimposed upon a yellow one — a Jewish homosexual.
Yellow triangle superimposed over a black inverted triangle, or "voided" black inverted triangle superimposed over a yellow triangle — an Aryan convicted of miscegenation and labeled as a "race defiler".
In addition to color-coding, some groups had to put letter insignia on their triangles to denote country of origin. Red triangle with a letter: "B" (Belgier, Belgians), "F" (Franzosen, French), "H" (Holländer, Dutch), "I" (Italiener, Italians), "N" (Norweger, Norwegians), "P" (Polen, Poles), "S" (Republikanische Spanier, Republican Spanish) "T" (Tschechen, Czechs), "U" (Ungarn, Hungarians).
Also, repeated offenders would receive bars over their stars, a different color for a different crime.
A political prisoner would have a red bar over his/her star or triangle
A habitual criminal would have a green bar
A foreign forced laborer would have a blue bar
A Jehovah's Witness would have a purple bar
A homosexual or sex offenders would have a pink bar
An "asocial" would have a black bar
A Roma (Gypsy) would have a brown bar
There were many markings and combinations. A prisoner would usually have at least two, and possibly more than six.
In some camps the Nacht und Nebel prisoners got painted with two big letters NN in yellow.
Penal battalion, penal company, etc., are military units consisting of convicted persons for which military service was either the assigned punishment or a voluntary replacement of imprisonment.
http://en.wikipedia.org/wiki/Nazi_concentration_camp_badges