No. Every solid shape has at least one face. The closest you will get is a sphere, which has no edges or vertices, but it still has a face.
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The question is ambiguous. An octagon is a 2-dimensional shape with 8 edges and 8 vertices. Does a 3-D octagonal shape mean one with 8 edges or 8 faces or vertices, or faces which are 2d octagons?
the vertices are the corners to the shape, so you count the corners to whatever shape.
It is a square based pyramid which has 5 faces, 8 edges and 5 vertices
tricontatetrahedron
A polyhedron (solid shape formed by plane faces) with four faces is called a tetrahedron.