Circumsphere Radius of Icosahedron Calculator

✖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 [l_e]

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✖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.ⓘ Circumsphere Radius of Icosahedron [r_c]

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Formula

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Circumsphere Radius of Icosahedron

Formula

`"r"_{"c"} = sqrt(10+(2*sqrt(5)))/4*"l"_{"e"}`

Example

`"9.510565m"=sqrt(10+(2*sqrt(5)))/4*"10m"`

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Circumsphere Radius of Icosahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

r_c = sqrt(10+(2*sqrt(5)))/4*l_e --> sqrt(10+(2*sqrt(5)))/4*10

Evaluating ... ...

r_c = 9.51056516295153

STEP 3: Convert Result to Output's Unit

9.51056516295153 Meter --> No Conversion Required

FINAL ANSWER

9.51056516295153 ≈ 9.510565 Meter <-- Circumsphere Radius of Icosahedron

(Calculation completed in 00.004 seconds)

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< 11 Circumsphere Radius of Icosahedron Calculators

Circumsphere Radius of Icosahedron given Surface to Volume Ratio

Go 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

Go 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 Insphere Radius

Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

Circumsphere Radius of Icosahedron given Total Surface Area

Go 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

Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))

Circumsphere Radius of Icosahedron given Volume

Go 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 Midsphere Radius

Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))

Circumsphere Radius of Icosahedron given Face Perimeter

Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12

Circumsphere Radius of Icosahedron given Perimeter

Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120

Circumsphere Radius of Icosahedron

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

Circumsphere Radius of Icosahedron given Space Diagonal

Go Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2

< 6 Radius of Icosahedron Calculators

Insphere Radius of Icosahedron given Total Surface Area

Go 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

Go 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

Go Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))

Circumsphere Radius of Icosahedron

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

Insphere Radius of Icosahedron

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

Midsphere Radius of Icosahedron

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

Circumsphere Radius of Icosahedron Formula

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

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 Circumsphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron calculator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron to calculate the Circumsphere Radius of Icosahedron, Circumsphere Radius of Icosahedron 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. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Icosahedron using this online calculator? To use this online calculator for Circumsphere Radius of Icosahedron, enter Edge Length of Icosahedron (l_e) and hit the calculate button. Here is how the Circumsphere Radius of Icosahedron calculation can be explained with given input values -> 9.510565 = sqrt(10+(2*sqrt(5)))/4*10.

FAQ

What is Circumsphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron 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 represented as r_c = sqrt(10+(2*sqrt(5)))/4*l_e or Circumsphere Radius of Icosahedron = sqrt(10+(2*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 Circumsphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron 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 is calculated using Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron. To calculate Circumsphere Radius of Icosahedron, you need Edge Length of Icosahedron (l_e). 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 Circumsphere Radius of Icosahedron?

In this formula, Circumsphere Radius of Icosahedron uses Edge Length of Icosahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -

Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
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
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)

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