Volume of Regular Icosahedron Calculator

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✖The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.ⓘ Side [s]

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✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of Regular Icosahedron [V]

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Credits

Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 1000+ more calculators!

Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Calculator and 1000+ more calculators!

Volume of Regular Icosahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

volume = (5*(3+sqrt(5))*Side^3)/12
V = (5*(3+sqrt(5))*s^3)/12
This formula uses 1 Functions, 1 Variables

Functions Used

sqrt - Squre root function, sqrt(Number)

Variables Used

Side - The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)

STEP 1: Convert Input(s) to Base Unit

Side: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (5*(3+sqrt(5))*s^3)/12 --> (5*(3+sqrt(5))*9^3)/12

Evaluating ... ...

V = 1590.45564816556

STEP 3: Convert Result to Output's Unit

1590.45564816556 Cubic Meter --> No Conversion Required

FINAL ANSWER

1590.45564816556 Cubic Meter <-- Volume

(Calculation completed in 00.016 seconds)

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< 10+ Volume Calculators

Volume of a Conical Frustum

volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go

Volume of a Capsule

volume = pi*((Radius)^2)*((4/3)*Radius+Height) Go

Volume of hollow cylinder

volume = pi*Height*(Radius 2^2-Radius 1^2) Go

Volume of a Circular Cone

volume = (1/3)*pi*(Radius)^2*Height Go

Volume of a Circular Cylinder

volume = pi*(Radius)^2*Height Go

Volume of a Rectangular Prism

volume = Width*Height*Length Go

Volume of a Hemisphere

volume = (2/3)*pi*(Radius)^3 Go

Volume of a Sphere

volume = (4/3)*pi*(Radius)^3 Go

Volume of a Pyramid

volume = (1/3)*Side^2*Height Go

Volume of a Cube

volume = Side^3 Go

< 6 Volume of Platonic Solids Calculators

Volume of Platonic Solids

volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle)) Go

Volume of Regular Dodecahedron

volume = ((15+(7*sqrt(5)))*Side^3)/4 Go

Volume of Regular Icosahedron

volume = (5*(3+sqrt(5))*Side^3)/12 Go

Volume of Regular Tetrahedron

volume = (Side^3)/(6*sqrt(2)) Go

Volume of Regular Octahedron

volume = (sqrt(2))*(Side^3)/3 Go

Volume of a Cube

volume = Side^3 Go

Volume of Regular Icosahedron Formula

volume = (5*(3+sqrt(5))*Side^3)/12
V = (5*(3+sqrt(5))*s^3)/12

How many edges does a icosahedron have?

There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. The icosahedron is the dual of the dodecahedron having three regular pentagonal faces around each vertex. The icosahedron represents the WATER element, symbolizing dreams, intuition, and emotions.

How to Calculate Volume of Regular Icosahedron?

Volume of Regular Icosahedron calculator uses volume = (5*(3+sqrt(5))*Side^3)/12 to calculate the Volume, Volume of Regular Icosahedron, is the amount of the space which the shapes takes up. Volume and is denoted by V symbol.

How to calculate Volume of Regular Icosahedron using this online calculator? To use this online calculator for Volume of Regular Icosahedron, enter Side (s) and hit the calculate button. Here is how the Volume of Regular Icosahedron calculation can be explained with given input values -> 1590.456 = (5*(3+sqrt(5))*9^3)/12.

FAQ

What is Volume of Regular Icosahedron?

Volume of Regular Icosahedron, is the amount of the space which the shapes takes up and is represented as V = (5*(3+sqrt(5))*s^3)/12 or volume = (5*(3+sqrt(5))*Side^3)/12. The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.

How to calculate Volume of Regular Icosahedron?

Volume of Regular Icosahedron, is the amount of the space which the shapes takes up is calculated using volume = (5*(3+sqrt(5))*Side^3)/12. To calculate Volume of Regular Icosahedron, you need Side (s). With our tool, you need to enter the respective value for Side 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?

In this formula, Volume uses Side. We can use 6 other way(s) to calculate the same, which is/are as follows -

volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle))
volume = Side^3
volume = ((15+(7*sqrt(5)))*Side^3)/4
volume = (5*(3+sqrt(5))*Side^3)/12
volume = (sqrt(2))*(Side^3)/3
volume = (Side^3)/(6*sqrt(2))

Where is the Volume of Regular Icosahedron calculator used?

Among many, Volume of Regular Icosahedron calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}

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