Midsphere Radius 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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✖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.ⓘ Midsphere Radius of Icosahedron given Insphere Radius [r_m]

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Formula

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Midsphere Radius of Icosahedron given Insphere Radius

Formula

`"r"_{"m"} = (1+sqrt(5))*(3*"r"_{"i"})/(sqrt(3)*(3+sqrt(5)))`

Example

`"7.493264m"=(1+sqrt(5))*(3*"7m")/(sqrt(3)*(3+sqrt(5)))`

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Midsphere Radius of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
r_m = (1+sqrt(5))*(3*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

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.
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

r_m = (1+sqrt(5))*(3*r_i)/(sqrt(3)*(3+sqrt(5))) --> (1+sqrt(5))*(3*7)/(sqrt(3)*(3+sqrt(5)))

Evaluating ... ...

r_m = 7.49326388523489

STEP 3: Convert Result to Output's Unit

7.49326388523489 Meter --> No Conversion Required

FINAL ANSWER

7.49326388523489 ≈ 7.493264 Meter <-- Midsphere Radius of Icosahedron

(Calculation completed in 00.021 seconds)

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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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< 11 Midsphere Radius of Icosahedron Calculators

Midsphere Radius of Icosahedron given Surface to Volume Ratio

Go 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

Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))

Midsphere Radius of Icosahedron given Circumsphere Radius

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

Midsphere Radius of Icosahedron given Insphere Radius

Go Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

Midsphere Radius of Icosahedron given Total Surface Area

Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(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)))

Midsphere Radius of Icosahedron given Face Area

Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))

Midsphere Radius of Icosahedron given Volume

Go 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

Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12

Midsphere Radius of Icosahedron given Perimeter

Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Perimeter of Icosahedron/120

Midsphere Radius of Icosahedron

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

Midsphere Radius of Icosahedron given Insphere Radius Formula

Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
r_m = (1+sqrt(5))*(3*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 Midsphere Radius of Icosahedron given Insphere Radius?

Midsphere Radius of Icosahedron given Insphere Radius calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Insphere 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 insphere radius of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (r_i) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Insphere Radius calculation can be explained with given input values -> 7.493264 = (1+sqrt(5))*(3*7)/(sqrt(3)*(3+sqrt(5))).

FAQ

What is Midsphere Radius of Icosahedron given Insphere Radius?

The Midsphere Radius of Icosahedron given Insphere 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 insphere radius of the Icosahedron and is represented as r_m = (1+sqrt(5))*(3*r_i)/(sqrt(3)*(3+sqrt(5))) or Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*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 Midsphere Radius of Icosahedron given Insphere Radius?

The Midsphere Radius of Icosahedron given Insphere 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 insphere radius of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Midsphere Radius 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 Midsphere Radius of Icosahedron?

In this formula, Midsphere Radius of Icosahedron uses Insphere 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
Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
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

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