# Solid

In the context of Geometry, a solid is a shape that occupies space and has volume and surface area. A solid has three dimensions, including length, width (or depth), and height. The following are some examples.

## Types of solids

While there are many different ways to categorize solids, solids are often divided into polyhedra (plural for polyhedron) and non-polyhedra. The following are some important polyhedra and non-polyhedra studied in Geometry.

### Polyhedron

A polyhedron is a solid whose faces are polygons. The word polyhedron has Greek origins, which loosely translates as "many faces." Prisms and pyramids are two of many types of polyhedra studied in geometry.

#### Prism

Prisms are polyhedra that have two congruent faces, called bases, that lie in parallel planes. The other faces (the sides that are not bases) are parallelograms, rectangles, or squares. A prism is typically named based on the shape of its polygonal bases. Below are three examples.

Rectangular prism | Hexagonal prism | Triangular prism |
---|---|---|

The bases are rectangles. | The bases are hexagons. | The bases are triangles. |

#### Pyramids

Pyramids are polyhedra that contain only one polygonal base; all the other faces are triangles. The triangular faces (aside from the base of a triangular pyramid) all share a common vertex called the apex. Like a prism, a pyramid is also typically named based on the shape of its polygonal base. Below are three examples of pyramids with different bases.

Square pyramid | Triangular pyramid | Hexagonal pyramid |
---|---|---|

The base is a square. | The base is a triangle. | The base is a hexagon. |

#### General polyhedra

Polyhedra are 3D shapes that can take on many other shapes. Below are two examples.

### Non-polyhedra

A non-polyhedron is a space figure that has at least one face or component that is not a polygon. In geometry, three types of non-polyhedra that are commonly studied are cylinders, cones, and spheres.

#### Cylinder

A cylinder is a 3D shape that is made up of two flat circular bases and a curved surface that "wraps" around the bases. The following are two examples.

#### Cone

A cone is a 3D shape that is made up of a circular base that tapers to a point. The following are two examples.

#### Sphere

A sphere is a 3D shape that has a round shape. All points on the surface of a sphere are equidistant from a point called the center.