STEP 0: Pre-Calculation Summary
Formula Used
rc = sqrt(10+(2*sqrt(5)))/4*(12*ri)/(sqrt(3)*(3+sqrt(5)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Circumsphere Radius of Icosahedron - (Measured in Meter) - Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Icosahedron: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(10+(2*sqrt(5)))/4*(12*ri)/(sqrt(3)*(3+sqrt(5))) --> sqrt(10+(2*sqrt(5)))/4*(12*7)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
rc = 8.80886000655373
STEP 3: Convert Result to Output's Unit
8.80886000655373 Meter --> No Conversion Required
8.80886000655373 8.80886 Meter <-- Circumsphere Radius of Icosahedron
(Calculation completed in 00.003 seconds)
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## Credits

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 11 Circumsphere Radius of Icosahedron Calculators

Circumsphere Radius of Icosahedron given Surface to Volume Ratio
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Circumsphere Radius of Icosahedron given Lateral Surface Area
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Circumsphere Radius of Icosahedron given Total Surface Area
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Circumsphere Radius of Icosahedron given Face Area
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Circumsphere Radius of Icosahedron given Volume
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Circumsphere Radius of Icosahedron given Face Perimeter
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
Circumsphere Radius of Icosahedron given Perimeter
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
Circumsphere Radius of Icosahedron given Space Diagonal
Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2

rc = sqrt(10+(2*sqrt(5)))/4*(12*ri)/(sqrt(3)*(3+sqrt(5)))

## 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.

Circumsphere Radius of Icosahedron given Insphere Radius calculator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the insphere radius of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Circumsphere Radius of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Circumsphere Radius of Icosahedron given Insphere Radius calculation can be explained with given input values -> 8.80886 = sqrt(10+(2*sqrt(5)))/4*(12*7)/(sqrt(3)*(3+sqrt(5))).

### FAQ

The Circumsphere Radius of Icosahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the insphere radius of the Icosahedron and is represented as rc = sqrt(10+(2*sqrt(5)))/4*(12*ri)/(sqrt(3)*(3+sqrt(5))) or Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
The Circumsphere Radius of Icosahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the insphere radius of the Icosahedron is calculated using Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Circumsphere Radius of Icosahedron given Insphere Radius, you need Insphere Radius of Icosahedron (ri). With our tool, you need to enter the respective value for Insphere Radius 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 Circumsphere Radius of Icosahedron?
In this formula, Circumsphere Radius of Icosahedron uses Insphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
• Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
• Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120 Let Others Know