Are cyclic products, such as $\prod_{cyc} a(b+c) = abc(a+b)(b+c)(c+a)$, a widely accepted notation?

Question

I know that a cyclic sum of three variables can be shortened like this: $$ab+bc+ca=\sum_{cyc} ab$$ Is it commonplace to do the same with products? That is, is the following an unambiguous notation? $$abc(a+b)(b+c)(c+a)=\prod_{cyc} a(b+c)$$