the pointy pyramid is just that a pyramid
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A 7 sided pyramid would be called a heptahedral or heptahedron.
Khafre Pyramid
It is the net of its solid shape. If the top of the pyramid is cut off parallel to the base, then it is a truncated pyramid, or a frustum.
=Pyramid=
No the "Pyramid Age" lasted from 2630 BC until about 1514 BC.