Volume of Icosahedron Calculator

✖Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.ⓘ Edge Length of Icosahedron [l_e]

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✖Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.ⓘ Volume of Icosahedron [V]

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Volume of Icosahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
V = 5/12*(3+sqrt(5))*l_e^3
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Volume of Icosahedron - (Measured in Cubic Meter) - Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.
Edge Length of Icosahedron - (Measured in Meter) - Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Icosahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/12*(3+sqrt(5))*l_e^3 --> 5/12*(3+sqrt(5))*10^3

Evaluating ... ...

V = 2181.69499062491

STEP 3: Convert Result to Output's Unit

2181.69499062491 Cubic Meter --> No Conversion Required

FINAL ANSWER

2181.69499062491 ≈ 2181.695 Cubic Meter <-- Volume of Icosahedron

(Calculation completed in 00.004 seconds)

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< Volume of Icosahedron Calculators

Volume of Icosahedron given Circumsphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Total Surface Area

LaTeX Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

< Volume of Icosahedron Calculators

Volume of Icosahedron given Circumsphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Total Surface Area

LaTeX Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

Volume of Icosahedron Formula

LaTeX Go

Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
V = 5/12*(3+sqrt(5))*l_e^3

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Icosahedron?

Volume of Icosahedron calculator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3 to calculate the Volume of Icosahedron, Volume of Icosahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

How to calculate Volume of Icosahedron using this online calculator? To use this online calculator for Volume of Icosahedron, enter Edge Length of Icosahedron (l_e) and hit the calculate button. Here is how the Volume of Icosahedron calculation can be explained with given input values -> 2181.695 = 5/12*(3+sqrt(5))*10^3.

FAQ

What is Volume of Icosahedron?

Volume of Icosahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron and is represented as V = 5/12*(3+sqrt(5))*l_e^3 or Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3. Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

How to calculate Volume of Icosahedron?

Volume of Icosahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron is calculated using Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3. To calculate Volume of Icosahedron, you need Edge Length of Icosahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Icosahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Icosahedron?

In this formula, Volume of Icosahedron uses Edge Length of Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

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