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A "pyramid" in geometry is a solid whose base is a polygon (many sided planar figure) and a vertex (a single point where all the triangular faces meet).

The base of a regular pyramid is a polygon whose sides all have the same length.

As such a pyramid can have any number of faces.

An equilateral pyramid (with all sides - including the sides meeting at the vertex - has sides of the same length) is necessarily regular and can have 4, 5, or 6 sides if the base is a triangle, square or pentagon.

The equilateral triangular pyramid is also called a regular tetrahedron.

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