Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal Calculator

✖Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Diagonal of Icosidodecahedron [d_Pentagon]

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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 Pentagonal Face Diagonal [r_m]

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Formula

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Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal

Formula

`"r"_{"m"} = sqrt(5+(2*sqrt(5)))*"d"_{"Pentagon"}/(1+sqrt(5))`

Example

`"15.2169m"=sqrt(5+(2*sqrt(5)))*"16m"/(1+sqrt(5))`

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Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Diagonal of Icosidodecahedron/(1+sqrt(5))
r_m = sqrt(5+(2*sqrt(5)))*d_Pentagon/(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.
Pentagonal Face Diagonal of Icosidodecahedron - (Measured in Meter) - Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagonal Face Diagonal 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)))*d_Pentagon/(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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< 11 Midsphere Radius of Icosidodecahedron Calculators

Midsphere Radius of Icosidodecahedron given Surface to Volume Ratio

Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*(3*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5))))

Midsphere Radius of Icosidodecahedron given Total Surface Area

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 Pentagonal Face Area

Go Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5))))

Midsphere Radius of Icosidodecahedron given Volume

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 Pentagonal Face Diagonal

Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Diagonal of Icosidodecahedron/(1+sqrt(5))

Midsphere Radius of Icosidodecahedron given Triangular Face Area

Go Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Triangular Face Area of Icosidodecahedron)/sqrt(3))

Midsphere Radius of Icosidodecahedron given Circumsphere Radius

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

Midsphere Radius of Icosidodecahedron given Triangular Face Height

Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Triangular Face Height of Icosidodecahedron/sqrt(3)

Midsphere Radius of Icosidodecahedron given Pentagonal Face Perimeter

Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Perimeter of Icosidodecahedron/10

Midsphere Radius of Icosidodecahedron given Triangular Face Perimeter

Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Triangular Face Perimeter of Icosidodecahedron/6

Midsphere Radius of Icosidodecahedron

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

Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal Formula

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Diagonal of Icosidodecahedron/(1+sqrt(5))
r_m = sqrt(5+(2*sqrt(5)))*d_Pentagon/(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 Pentagonal Face Diagonal?

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

How to calculate Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal using this online calculator? To use this online calculator for Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal, enter Pentagonal Face Diagonal of Icosidodecahedron (d_Pentagon) and hit the calculate button. Here is how the Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal 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 Pentagonal Face Diagonal?

Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line to that sphere, and calculated using the pentagonal face diagonal of the Icosidodecahedron and is represented as r_m = sqrt(5+(2*sqrt(5)))*d_Pentagon/(1+sqrt(5)) or Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Diagonal of Icosidodecahedron/(1+sqrt(5)). Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.

How to calculate Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal?

Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line to that sphere, and calculated using the pentagonal face diagonal of the Icosidodecahedron is calculated using Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Diagonal of Icosidodecahedron/(1+sqrt(5)). To calculate Midsphere Radius of Icosidodecahedron given Pentagonal Face Diagonal, you need Pentagonal Face Diagonal of Icosidodecahedron (d_Pentagon). With our tool, you need to enter the respective value for Pentagonal Face Diagonal 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 Pentagonal Face Diagonal of Icosidodecahedron. We can use 10 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)
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5))
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*(3*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5))))
Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Triangular Face Area of Icosidodecahedron)/sqrt(3))
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Triangular Face Perimeter of Icosidodecahedron/6
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Triangular Face Height of Icosidodecahedron/sqrt(3)
Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5))))
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Pentagonal Face Perimeter of Icosidodecahedron/10

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