Midsphere Radius of Icosidodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Icosidodecahedron [r_c]

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✖Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Icosidodecahedron given Circumsphere Radius [r_m]

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Midsphere Radius of Icosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5))
r_m = sqrt(5+(2*sqrt(5)))*r_c/(1+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 Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.
Circumsphere Radius of Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Icosidodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = sqrt(5+(2*sqrt(5)))*r_c/(1+sqrt(5)) --> sqrt(5+(2*sqrt(5)))*16/(1+sqrt(5))

Evaluating ... ...

r_m = 15.2169042607225

STEP 3: Convert Result to Output's Unit

15.2169042607225 Meter --> No Conversion Required

FINAL ANSWER

15.2169042607225 ≈ 15.2169 Meter <-- Midsphere Radius of Icosidodecahedron

(Calculation completed in 00.020 seconds)

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< Midsphere Radius of Icosidodecahedron Calculators

Midsphere Radius of Icosidodecahedron given Total Surface Area

LaTeX Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Midsphere Radius of Icosidodecahedron given Volume

LaTeX Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

Midsphere Radius of Icosidodecahedron given Circumsphere Radius

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

Midsphere Radius of Icosidodecahedron

LaTeX Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron

Midsphere Radius of Icosidodecahedron given Circumsphere Radius Formula

LaTeX Go

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

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Midsphere Radius of Icosidodecahedron given Circumsphere Radius?

Midsphere Radius of Icosidodecahedron given Circumsphere Radius calculator uses Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)) to calculate the Midsphere Radius of Icosidodecahedron, Midsphere Radius of Icosidodecahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the circumsphere radius of the Icosidodecahedron. Midsphere Radius of Icosidodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Icosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Icosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Icosidodecahedron (r_c) and hit the calculate button. Here is how the Midsphere Radius of Icosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 15.2169 = sqrt(5+(2*sqrt(5)))*16/(1+sqrt(5)).

FAQ

What is Midsphere Radius of Icosidodecahedron given Circumsphere Radius?

Midsphere Radius of Icosidodecahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the circumsphere radius of the Icosidodecahedron and is represented as r_m = sqrt(5+(2*sqrt(5)))*r_c/(1+sqrt(5)) or Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)). Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

How to calculate Midsphere Radius of Icosidodecahedron given Circumsphere Radius?

Midsphere Radius of Icosidodecahedron given Circumsphere Radius formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the circumsphere radius of the Icosidodecahedron is calculated using Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)). To calculate Midsphere Radius of Icosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Icosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Icosidodecahedron 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 Icosidodecahedron?

In this formula, Midsphere Radius of Icosidodecahedron uses Circumsphere Radius of Icosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

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