This tool is designed to calculate the volume of a regular icosahedron. It is particularly useful for students, educators, and anyone interested in 3D geometry. Use this calculator to quickly find the volume based on the length of a side.
Icosahedron Volume Calculator
Results
The volume of the icosahedron is: 0 cubic units.
Data Source and Methodology
This calculator uses the standard formula for calculating the volume of a regular icosahedron. All calculations are based on this formula.
The Formula Explained
Glossary of Variables
- V: Volume of the icosahedron.
- a: Length of a side of the icosahedron.
How It Works: A Step-by-Step Example
For example, if the side length is 2 units, the volume is calculated as follows:
\( V = \frac{5}{12} \times (3 + \sqrt{5}) \times 2^3 = 17.4532 \) cubic units.
Frequently Asked Questions (FAQ)
What is an icosahedron?
An icosahedron is a polyhedron with 20 faces, all of which are equilateral triangles.
How is the volume calculated?
The volume is calculated using the formula: \( V = \frac{5}{12} \times (3 + \sqrt{5}) \times a^3 \).
Why is this calculator useful?
This calculator provides a quick and accurate way to determine the volume of a regular icosahedron.
Can I use this tool for irregular icosahedrons?
No, this tool is specifically for regular icosahedrons where all sides are equal.
What units should be used?
You can use any unit for the side length, but ensure that the volume will be in cubic units of the same type.
Formula (LaTeX) + variables + units
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\( V = \frac{5}{12} \times (3 + \sqrt{5}) \times a^3 \)
- T = property tax (annual or monthly depending on input) (currency)
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
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