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# Calculate The Volume of An Icosahedron

Last updated: Saturday, June 24, 2023
Select a type of polyhedron below
Tetrahedron
Hexahedron
Octahedron
Dodecahedron
Icosahedron

An icosahedron is a three-dimensional geometric figure with twenty equilateral triangular faces. As one of the five Platonic solids, it has unique properties in geometry, making it relevant across various fields such as mathematics, engineering, and design. Studying icosahedra contributes to our understanding of symmetry, shape, and the interrelationships between different geometrical structures.

Real-life examples of objects with an icosahedron shape can be found in numerous contexts. In the world of sports, icosahedron-shaped dice are popular for their fair, unbiased rolling properties. In virology, many viruses, such as the common cold and HIV, have an icosahedral capsid structure for efficient packing of genetic material. In art and design, icosahedra are often used in sculptures and geometric decorations for their visually captivating appearance and inherent balance.

In mathematics, the study of icosahedra and other polyhedra helps deepen our understanding of three-dimensional geometry and its practical applications. The icosahedron is the dual polyhedron of the dodecahedron, meaning it can be formed by connecting the centers of the faces of a dodecahedron. In engineering and computer graphics, icosahedra can be used as building blocks for creating more complex shapes through a process called meshing, dividing irregular shapes into smaller elements for easier analysis and rendering.

Easily calculate the volume of an icosahedron with step-by-step guidance using our free calculator below.

The formula for determining the volume of an icosahedron is defined as:
$$V$$ $$=$$ $$\dfrac{5 \cdot (3 + \sqrt{5})}{12} \cdot a^3$$
$$V$$: the volume of the icosahedron
$$a$$: the length of any side
The SI unit of volume is: $$cubic \text{ } meter\text{ }(m^3)$$

## Find $$V$$

Use this calculator to determine the volume of an icosahedron when the length of any side is given.
Hold & Drag
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the length of any side
$$a$$
$$meter$$
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