The fixed point at the intersection of all the faces of the pyramid is called the VERTEX of the pyramid.
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A hexagonal pyramid has 6 triangular faces that meet at a point. It has 6 triangles and 1 hexagonal base.
A square pyramid is a polyhedron with a square base and triangular sides that meet at a point at the top. This gives this pyramid five faces.
pyramid
The object you are describing is a square pyramid. A square pyramid has a square base and four triangular faces that meet at a single point called the apex. Each triangular face is formed by connecting a vertex of the base square to the apex. The total number of faces in a square pyramid is 5 - 1 square base and 4 triangular faces.
4 sided (or perhaps 5 if you count the base). The base is a square and the four triangular faces rise off each of the 4 edges and meet in a point at the top.