Edge Length of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
le = (12*ri)/(sqrt(3)*(3+sqrt(5)))
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
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.
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
le = (12*ri)/(sqrt(3)*(3+sqrt(5))) --> (12*7)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
le = 9.26218353549451
STEP 3: Convert Result to Output's Unit
9.26218353549451 Meter --> No Conversion Required
FINAL ANSWER
9.26218353549451 9.262184 Meter <-- Edge Length of Icosahedron
(Calculation completed in 00.022 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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Verified by Nayana Phulphagar
Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
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11 Edge Length of Icosahedron Calculators

Edge Length of Icosahedron given Surface to Volume Ratio
​ Go Edge Length of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Edge Length of Icosahedron given Circumsphere Radius
​ Go Edge Length of Icosahedron = (4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Edge Length of Icosahedron given Lateral Surface Area
​ Go Edge Length of Icosahedron = sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Edge Length of Icosahedron given Insphere Radius
​ Go Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Edge Length of Icosahedron given Space Diagonal
​ Go Edge Length of Icosahedron = (2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Edge Length of Icosahedron given Total Surface Area
​ Go Edge Length of Icosahedron = sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Edge Length of Icosahedron given Face Area
​ Go Edge Length of Icosahedron = sqrt((4*Face Area of Icosahedron)/sqrt(3))
Edge Length of Icosahedron given Volume
​ Go Edge Length of Icosahedron = ((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
Edge Length of Icosahedron given Midsphere Radius
​ Go Edge Length of Icosahedron = (4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Edge Length of Icosahedron given Face Perimeter
​ Go Edge Length of Icosahedron = Face Perimeter of Icosahedron/3
Edge Length of Icosahedron given Perimeter
​ Go Edge Length of Icosahedron = Perimeter of Icosahedron/30

Edge Length of Icosahedron given Insphere Radius Formula

Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
le = (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.

How to Calculate Edge Length of Icosahedron given Insphere Radius?

Edge Length of Icosahedron given Insphere Radius calculator uses Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Edge Length of Icosahedron, The Edge Length of Icosahedron given Insphere Radius formula is defined as the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Edge Length of Icosahedron is denoted by le symbol.

How to calculate Edge Length of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Edge Length of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Edge Length of Icosahedron given Insphere Radius calculation can be explained with given input values -> 9.262184 = (12*7)/(sqrt(3)*(3+sqrt(5))).

FAQ

What is Edge Length of Icosahedron given Insphere Radius?
The Edge Length of Icosahedron given Insphere Radius formula is defined as the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron and is calculated using the insphere radius of the Icosahedron and is represented as le = (12*ri)/(sqrt(3)*(3+sqrt(5))) or Edge Length of Icosahedron = (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.
How to calculate Edge Length of Icosahedron given Insphere Radius?
The Edge Length of Icosahedron given Insphere Radius formula is defined as the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron and is calculated using the insphere radius of the Icosahedron is calculated using Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Edge Length 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 Edge Length of Icosahedron?
In this formula, Edge Length of Icosahedron uses Insphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Edge Length of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Edge Length of Icosahedron = (4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Edge Length of Icosahedron = (4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
  • Edge Length of Icosahedron = (2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Edge Length of Icosahedron = sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
  • Edge Length of Icosahedron = ((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
  • Edge Length of Icosahedron = Face Perimeter of Icosahedron/3
  • Edge Length of Icosahedron = sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Edge Length of Icosahedron = sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Edge Length of Icosahedron = Perimeter of Icosahedron/30
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