One possibility is a heptagonal pyramid - with a heptagon as a base and seven triangular faces meeting at the apex.
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A pentagonal pyramid.
If you mean a pyramid with a four sided base, it is a square pyramid. If you mean one with four faces, it is a tetrahedron.
well actually it is a prism. If you mean a 5 sided pyramid with the 6 side being the bottom it would be called a Pentagonal Pyramid
A 8 sided polygon is called a octagon.
An eight sided shape is called an octagon.