# Pyramid

## What is Pyramid?

pyramid is a polyhedron whose surface is formed by a base that is any polygon and triangular lateral faces that meet at a vertex called the apex (or vertex of the pyramid). Pyramids have as many triangles on their side faces as there are sides on the base.

## Elements of the pyramid

In a pyramid the following elements can be differentiated :

• Base ( B ): any polygon. It is the only face that does not touch the vertex of the pyramid.
• Faces ( C ): the triangles on the sides and the base.
• Edges ( a ): segments where two faces of the pyramid meet. We can distinguish lateral edges, which are those that reach the vertex (or apex), and basic edges, which are at the base.
• Height ( h ): distance from the plane of the base to the vertex of the pyramid.
• Vertex of the pyramid ( V ): point where the triangular lateral faces converge. Also called the apex.
• Apothem of the pyramid ( ap ): distance from the vertex to one side of the base. It only exists in regular pyramids. Since in this case, the lateral faces are isosceles, the apothem of the pyramid is also the height of the lateral faces.
• Apothem of the base ( ap b ): distance from one side of the base to the center of it. It only exists in regular pyramids.

## Types of pyramid

The pyramids can be categorized by four criteria:

### Number of sides of the base

The pyramids can be classified according to the number of sides that have their basis :

• Triangular pyramid: the base is a triangle (3 sides).
• Pentagonal pyramid: the base is a pentagon (5 sides).
• Hexagonal pyramid: the base is a hexagon (6 sides)

### Regular or irregular

• Regular pyramid: a pyramid is regular if the base is a regular polygon and in turn is a square pyramid. The lateral faces are isosceles triangles and equal to each other.
• Irregular pyramid: when the base is an irregular polygon or it is an oblique pyramid .

### Straight or oblique

• Right pyramid: the pyramid is straight when all its lateral faces are isosceles triangles. In this case, the line perpendicular to the base that passes through the vertex of the pyramid cuts the base through the center of the polygon.
• Oblique Pyramid: The pyramid is oblique when not all lateral triangles are isosceles.

### Straight or oblique

• Right pyramid: the pyramid is straight when all its lateral faces are isosceles triangles. In this case, the line perpendicular to the base that passes through the vertex of the pyramid cuts the base through the center of the polygon.
• Oblique Pyramid: The pyramid is oblique when not all lateral triangles are isosceles.