A triangular pyramid, square pyramid, triangular prism,rectangular prism,septagonal prism. Anything that has more than corner.
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polyhedra
There are infinitely many shapes. Among them are polyhedra, with four or more vertices.
octahedron * * * * * OCTAHEDRON has 8 letters??? I make it 10. How about TRIANGLE?
A cone has one vertex and one edge.
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).