## Midsphere Radius of Icosahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron
rm = (1+sqrt(5))/4*le
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
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.
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
rm = (1+sqrt(5))/4*le --> (1+sqrt(5))/4*10
Evaluating ... ...
rm = 8.09016994374947
STEP 3: Convert Result to Output's Unit
8.09016994374947 Meter --> No Conversion Required
8.09016994374947 8.09017 Meter <-- Midsphere Radius of Icosahedron
(Calculation completed in 00.004 seconds)
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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

## < 6 Radius of Icosahedron Calculators

Insphere Radius of Icosahedron given Total Surface Area
Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*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)
Midsphere Radius of Icosahedron given Space Diagonal
Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron

## Midsphere Radius of Icosahedron Formula

Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron
rm = (1+sqrt(5))/4*le

## 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 Midsphere Radius of Icosahedron?

Midsphere Radius of Icosahedron calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere. Midsphere Radius of Icosahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Icosahedron using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron, enter Edge Length of Icosahedron (le) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron calculation can be explained with given input values -> 8.09017 = (1+sqrt(5))/4*10.

### FAQ

What is Midsphere Radius of Icosahedron?
The Midsphere Radius of Icosahedron 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 represented as rm = (1+sqrt(5))/4*le or Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron. 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 Midsphere Radius of Icosahedron?
The Midsphere Radius of Icosahedron formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron. To calculate Midsphere Radius of Icosahedron, you need Edge Length of Icosahedron (le). 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 Midsphere Radius of Icosahedron?
In this formula, Midsphere Radius of Icosahedron uses Edge Length of Icosahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))
• Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
• Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
• Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
• Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12
• Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
• Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
• Midsphere Radius of Icosahedron = (1+sqrt(5))*Perimeter of Icosahedron/120
• Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))
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