The Kronecker coefficients arise when one wants to decompose the tensor product of two irreducible complex representations of the symmetric group on a finite set. One way to study these coefficients is to be interested in the Kronecker cone, which will be defined in this talk. We will then explain how to produce particular faces of this cone, formed of what are called "stable triples" (a notion defined by J. Stembridge in 2014). This will extend results obtained independently by L. Manivel and E. Vallejo in 2015.