STEP 0: Pre-Calculation Summary
Formula Used
rm = (1+sqrt(5))*rc/(sqrt(10+(2*sqrt(5))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Midsphere Radius of Icosahedron - (Measured in Meter) - The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.
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.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Icosahedron: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = (1+sqrt(5))*rc/(sqrt(10+(2*sqrt(5)))) --> (1+sqrt(5))*9/(sqrt(10+(2*sqrt(5))))
Evaluating ... ...
rm = 7.65585727516836
STEP 3: Convert Result to Output's Unit
7.65585727516836 Meter --> No Conversion Required
7.65585727516836 7.655857 Meter <-- Midsphere 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 Midsphere Radius of Icosahedron Calculators

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

rm = (1+sqrt(5))*rc/(sqrt(10+(2*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.

Midsphere Radius of Icosahedron given Circumsphere Radius calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))) to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the circumsphere radius of the Icosahedron. Midsphere Radius of Icosahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Icosahedron (rc) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 7.655857 = (1+sqrt(5))*9/(sqrt(10+(2*sqrt(5)))).

### FAQ

The Midsphere Radius of Icosahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the circumsphere radius of the Icosahedron and is represented as rm = (1+sqrt(5))*rc/(sqrt(10+(2*sqrt(5)))) or Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))). 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.
The Midsphere Radius of Icosahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the circumsphere radius of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))). To calculate Midsphere Radius of Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Icosahedron (rc). With our tool, you need to enter the respective value for Circumsphere 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 Midsphere Radius of Icosahedron?
In this formula, Midsphere Radius of Icosahedron uses Circumsphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
• Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron