# reference request – Name of the facet of a cone containing all edges except one

Let $$C subseteq mathbb R ^ n$$ to be a polyhedral cone, thus generated by its edges ($$1$$(three-dimensional faces) and $$F subseteq C$$ a facet (codimension $$1$$ face) containing all edges except $$e$$. In particular, the map $$F times e stackrel {+} { to} C$$ is an isomorphism of the cones.

Is there a name for this property of $$F$$ or $$e$$ (who are determined)?

Essentially, I consider the edges $$e$$ like this as a kind of trivial, and would like to separate them to deal with the difficult part of $$C$$. So maybe we could talk about a "main facet" $$F$$ of $$C$$and let the "core of $$C$$"is the intersection of the" main facets ". Then the map $$core (C) times production _ { text {core edge} e} e stackrel {+} { to} C$$ would be an isomorphism, and $$core (C)$$ would have no basic edges.

There is a similar and familiar construction in the theory of simplicial complexes, where a "cone-top" $$v$$ of $$Delta$$ is a lying in each maximum face. You can safely remove all the vertices of the cones, and recreate them $$Delta$$. Obviously, we do not want to steal this terminology directly and talk about "conical edges".