This viewer lets you explore the configuration of regular convex faces around a vertex (the apex). You can control the number of faces N around the apex and for each face, you can set its number of vertices and its dihedral angle with the next face. The dihedral angles for the last two faces is computed from the configurations of all the previous faces.
Incidentally, the minimal value for N is 3 and then, there is no degree of freedom so no slider for the dihedral angles.
This three.js viewer was inspired by http://stemkoski.github.io/Three.js/ by Lee Stemkoski.