Oh, dude, you're talking about a square pyramid! It's like a pyramid, but with a square base and four triangular faces. So, technically, it has 5 faces in total. Math can be fun, right?
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a pyramid, in the sense that most people think of has a square base, with 4 triangle 'sides', which would be 5 faces. A regular tetrahedron has 4 equilateral triangles as faces.
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.
Lateral faces are the number of faces excluding the base. Since the square is the base, the other 4 sides will each be touching a lateral face to form a square pyramid (or it wont be a pyramid). So, there are 4.
A polyhedron can have any number of faces 4 or higher.
A pyramid can have 4 or more faces. A pyramid, with a n-sided polygon as base will have n+1 faces. The polygon with the least number of sides is a triangle and a triangular pyramid (tetrahedron) has 4 faces. A square based pyramid has 5 faces, and so on.