Edge Length of Icosahedron given Insphere Radius Calculator

✖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.ⓘ Insphere Radius of Icosahedron [r_i]

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✖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.ⓘ Edge Length of Icosahedron given Insphere Radius [l_e]

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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)))
l_e = (12*r_i)/(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

l_e = (12*r_i)/(sqrt(3)*(3+sqrt(5))) --> (12*7)/(sqrt(3)*(3+sqrt(5)))

Evaluating ... ...

l_e = 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 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Edge Length of Icosahedron Calculators

Edge Length of Icosahedron given Surface to Volume Ratio

LaTeX Go Edge Length of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Edge Length of Icosahedron given Circumsphere Radius

LaTeX Go Edge Length of Icosahedron = (4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))

Edge Length of Icosahedron given Insphere Radius

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

Edge Length of Icosahedron given Midsphere Radius

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

Edge Length of Icosahedron given Insphere Radius Formula

LaTeX Go

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

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