Im here to answer your question-
possibly a cone.
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and give you the wrong answer. A cone is a shape with 1 vertex: not MORE THAN 1 vertex! All polyhedra have more than 1 vertices.
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One possible answer is an infinite cone. Spheres have one face but no vertex. No physical 3-D shape can have a vertex without having more than one face (a real cone typically has two: side and bottom).
1 vertex less than a hexagon is a pentagon. 2 angles more than a triangle is a pentagon.
A cone has one vertex and one edge.
The Cone
Most of them. Cubes, prisms, pyramids, and all the -hedrons. Roundish things, like cones, spheres, hemispheres and cylinders don't have them.