There are an infinite number of shapes.
A tetrahedron (triangular pyramid), a square-based pyramid, a pentagonal pyramid, a hexagonal pyramid, etc.
A triangular prism, a rectangular prism (cuboid), a pentagonal prism, etc are some examples.
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3d shapes with plane faces are called polyhedra (singular = polyhedron). The minimum number of vertices is 4, there is no maximum.
a coneA cone.
Cone
A cone seems to fit the given description
There are a great many of them. One nice one is the icosahedron, which has 20 vertices and 11 letters.