A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
8 edges
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Faces: 5 Edges: 8
If side refers to 'face', then the pyramid would be a quadrilateral pyramid with 8 edges. If side refers to the base of the pyramid, it would be a pentagonal pyramid with 10 edges.
"Tetrahedral" is an adjective. It needs a noun associated with it before it can be an abject that may have edges.
A triangle has one face, three vertices and three edges.
If they were square they would take up more area and the edges may get in the way or take up space, also if you had a square head then it would be easier for the metal to get stripped or deformed which would make it harder for the tool to loosen it. If the head was round, the you couldn't get a tool to grip the edges of it, so you couldn't screw it in good or loosen it. Basically, hexagonal is the most efficient shape for a nut.