MATHEMATICS

Calculator for Icosahedron Volume

This calculator will help you find the volume of a icosahedron. The formula used in this calculator is listed below.

To use this calculator, you will need to know the edge length.

To give you a better mental model of the icosahedron, you can look at the visualization below. You can navigate the 3d-model of the icosahedron as you like.

Results

Volume = 2,181.695

You might also be interested in calculating the Surface Area for an Icosahedron

Icosahedron Volume Formula

Formula variable explanation:

  • I represents the volume.
  • a represents the Edge length.

LaTeX formula

If you are working in a TeX based editor you could use this TeX formula to calculate the icosahedron volume.

I=\frac{5}{12}\cdot{ a}^{3}\cdot\left(3+\sqrt{5}\right)

How To Calculate The Icosahedron Volume Your Self

Calculating the volume is rather simple when you know the formula presented above. Follow these steps:

  1. Write down this formula:

  2. Then change the following variables with your values:
    1. a shall be changed with the Edge length of your icosahedron. As an example a could be changed to 10.
  3. Now you can enter this in to your calculator and you will get your answer.

Icosahedron Characteristics

The following are properties of a icosahedron:

  • Icosahedron comes from the Greek words εἴκοσι (eíkosi) meaning twenty, and ἕδρα (hédra) meaning seat.
  • The regular icosahedron have 20 faces, 30 edges and 12 vertices.
  • The regular icosahedron have five equilateral triangular faces meeting at each vertex.
  • A regular icosahedron is one of five platonic solids.
  • Of the five platonic solids, the regular icosahedron is the one with the most faces and the largest volume for its surface area.
  • Each face of the icosahedron is a regular triangle.