How to use the "Facet" battery to make a geometric surface on a curved surface?

What means formula? If by that you mean the “components” as shown … have in mind that these are 100% C# . Meaning that if you are not quite familiar with coding they can’t help you at all (because for you they’ll be just a bunch of weird/freaky black boxes).

Other than that … well … in general there’s another big issue related with these “solids” of yours: offseting polylines inwards [if the mapped poly is in some sort of concave surf segment] and then bridge them properly in order to do the sides of the solids (where these polylines - in most of cases - have some tiny segments [blame the Voronoi approach for that - V is totally unsuitable for any rational real-life AEC result]).

BTW: See the offset issue here (what Rhino Methods do, that is):

And this is the correct way to do it: