Midsphere Radius of Icosahedron given Circumsphere Radius Calculator

✖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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✖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 Circumsphere Radius [r_m]

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Midsphere Radius of Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Icosahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (1+sqrt(5))*r_c/(sqrt(10+(2*sqrt(5)))) --> (1+sqrt(5))*9/(sqrt(10+(2*sqrt(5))))

Evaluating ... ...

r_m = 7.65585727516836

STEP 3: Convert Result to Output's Unit

7.65585727516836 Meter --> No Conversion Required

FINAL ANSWER

7.65585727516836 ≈ 7.655857 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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< Midsphere Radius of Icosahedron Calculators

Midsphere Radius of Icosahedron given Circumsphere Radius

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

Midsphere Radius of Icosahedron given Insphere Radius

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

Midsphere Radius of Icosahedron given Space Diagonal

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

Midsphere Radius of Icosahedron

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

Midsphere Radius of Icosahedron given Circumsphere Radius Formula

LaTeX Go

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

Midsphere Radius of Icosahedron given Circumsphere Radius calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))) to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Icosahedron (r_c) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 7.655857 = (1+sqrt(5))*9/(sqrt(10+(2*sqrt(5)))).

FAQ

What is Midsphere Radius of Icosahedron given Circumsphere Radius?

The Midsphere Radius of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron and is represented as r_m = (1+sqrt(5))*r_c/(sqrt(10+(2*sqrt(5)))) or Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))). 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.

How to calculate Midsphere Radius of Icosahedron given Circumsphere Radius?

The Midsphere Radius of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))). To calculate Midsphere Radius of Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Icosahedron (r_c). With our tool, you need to enter the respective value for Circumsphere 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 Circumsphere Radius of Icosahedron. We can use 3 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))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))

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