Singular locus of orientable 3-orbifolds Any reference (or any hints if the proof is easy) for the proof that the singular locus of a 3-dimensional orientable orbifold is a trivalent graph with each edge labelled by integers $a,b,c>1$ and if edges meet at a vertex then $1/a+1/b+1/c>1$ namely, there is a nbhd of the vertex which is a cone over an orientable spherical 2-orbifold?

Yes, it is easy. Use classification of 2-dimensional oriented spherical orbifolds.

Edit: every n-dimensional orbifold is locally a cone over a spherical orbifold of dimension n-1. Every spherical 2-dimensional oriented orbifold is either the sphere with two cone points or sphere with three cone points satisfying the inequality you mentioned (sum of inverses of their orders is $>1$).