How can I perform a trigonal bevel?

Pick any vertex of a default cube. Then, replace that vertex with a triangle, normal to the center of the cube, which connects the other edges.

Then you've described the "triangular" bevel I'm hoping to achieve, but how do I go about doing that? When I select one and only one vertex in blender, then hit ctrl+b, nothing happens. Is there some configuration for bevel I can set up so that blender creates a flat triangle bevel where the vertex on the cube used to be?