Hexahedron

A hexahedron is a polyhedron with 6 faces. In simple words, we can say that a hexahedron is a three-dimensional figure that has six faces. Some of its common examples are cube, cuboid, parallelepiped, Quadrilateral frustum, etc. A cube is a regular hexahedron that has all faces as equal squares with three squares meeting at each vertex. A regular hexahedron is one of the platonic solids. It has six faces, twelve edges, and eight vertices.

In this article, we will discuss the concept of a hexahedron and its properties and formula. We will understand its shape with the help of an image of its net and solve examples based on a hexahedron for a better understanding of the concept.

A hexahedron is a polyhedron with six faces. A regular hexahedron has six square faces and hence it is also called a cube. All interior angles of a regular hexahedron are equal to 90 degrees. It is six faces, twelve edges, and eight vertices. We can have different hexahedrons such as cuboids, trapezoidal prism, parallelepiped, rhombohedron, etc.

The net of a three-dimensional figure in geometry is a two-dimensional figure that when folded as per the given format gives a 3D shape. The net of a solid shape also helps to visualize solid shapes. The image below shows a regular hexahedron and its net showing all six faces of the hexahedron. When the two-dimensional net of the cube is folded, it gives a three-dimensional regular hexahedron.

Since a hexahedron can be of different types, let us discuss the formula to find the surface area and volume of a regular hexahedron. If a regular hexahedron (cube) has all edges of length 'a' units. Then, the formula for its lateral surface area, total surface area, and volume are:

• Lateral Surface Area of Regular Hexahedron = 4a² square units
• Total Surface Area of Regular Hexahedron = 6a² square units
• Volume of Regular Hexahedron = a³ cubic units

Now that we have understood the meaning of a hexahedron, let us go through some of its important properties below:

• It has six faces.
• It has eight vertices.
• It has twelve edges.
• A regular hexahedron has all faces as equal squares and is called a cube.
• The surface area of a regular hexahedron is 6a² square units, where 'a' is the side length of the cube.
• A regular hexahedron is one of the platonic solids.
• Three squares of a regular hexahedron meet at each vertex.
• The angles between any two faces or surfaces are 90°.
• The opposite faces and edges of a regular hexahedron are parallel to each other.

Important Notes on Hexahedron

• A hexahedron has six faces.
• A regular hexahedron has all six faces as squares and is called a cube.
• The lateral surface area, total surface area, and volume of a regular hexahedron with side length 'a' are given by, 4a² square units, 6a² square units, and a³ cubic units, respectively.

☛ Related Articles:

• Octahedron
• Tetrahedron
• Icosahedron

What is Hexahedron in Geometry?

A hexahedron is a polyhedron with 6 faces. In other words, we can say that a hexahedron is a three-dimensional figure that has six faces.

What Is Another Name for Hexahedron?

Another name for a hexahedron with all six faces as squares is cube. A cube is a three-dimensional figure that has six faces and all faces are squares of equal length.

What Does a Hexahedron Look Like?

A hexahedron is a polyhedron with six faces. If all faces of a hexahedron are squares, then it looks like a cube. Some other common examples of hexahedron are cuboid, parallelepiped, trapezoidal prism, etc.

What is a Regular Hexahedron?

A regular hexahedron is a three-dimensional shape with six faces and all faces are squares of equal length. The angle made by each face with another is a 90-degree angle.

How Many Faces Does a Hexahedron Have?

A hexahedron has six faces. It can be understood by its name as it has ' hex' which means six.

How to Find Volume of Hexahedron?

We can find the volume of a regular hexahedron with a side length of 'a' units using the formula, Volume = a³ cubic units.

How to Find the Surface Area of a Hexahedron?

We can find the total surface area and lateral surface area of a hexahedron using the following formulas:

• Lateral Surface Area of Regular Hexahedron = 4a² square units
• Total Surface Area of Regular Hexahedron = 6a² square units

Is Every Hexahedron a Cube?

No, every hexahedron is not a cube but every cube is a hexahedron. The necessary condition of a hexahedron is to have six faces but they need not be square. Since a cube has six faces, therefore we can call it a hexahedron.