A quadrilateral based pyramid (the base has four sides).
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A cube
It is a cube.
This is an impossible three-dimensional figure. A pyramid has 5 faces and 8 edges but has 5 corners, not 4. A 4-cornered three-dimensional figure has only one itteration: that of a 4 sided pyramid of 6 edges. Since your shape is 5 sided with 8 edges I would say you have got a number wrong there somewhere.
A cube
A pyramid with a square base.