Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter Calculator

✖Triangular Face Perimeter of Icosidodecahedron is the total length of all the boundary lines of any of the triangular faces of the Icosidodecahedron.ⓘ Triangular Face Perimeter of Icosidodecahedron [P_Triangle]

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✖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 given Triangular Face Perimeter [r_c]

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Formula

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Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter

Formula

`"r"_{"c"} = (1+sqrt(5))*"P"_{"Triangle"}/6`

Example

`"16.18034m"=(1+sqrt(5))*"30m"/6`

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Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6
r_c = (1+sqrt(5))*P_Triangle/6
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 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.
Triangular Face Perimeter of Icosidodecahedron - (Measured in Meter) - Triangular Face Perimeter of Icosidodecahedron is the total length of all the boundary lines of any of the triangular faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Triangular Face Perimeter of Icosidodecahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (1+sqrt(5))*P_Triangle/6 --> (1+sqrt(5))*30/6

Evaluating ... ...

r_c = 16.1803398874989

STEP 3: Convert Result to Output's Unit

16.1803398874989 Meter --> No Conversion Required

FINAL ANSWER

16.1803398874989 ≈ 16.18034 Meter <-- Circumsphere Radius of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 11 Circumsphere Radius of Icosidodecahedron Calculators

Circumsphere Radius of Icosidodecahedron given Surface to Volume Ratio

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*(3*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5))))

Circumsphere Radius of Icosidodecahedron given Total Surface Area

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Area

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*sqrt((Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5))))

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height

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

Circumsphere Radius of Icosidodecahedron given Midsphere Radius

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

Circumsphere Radius of Icosidodecahedron given Triangular Face Area

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*sqrt(Triangular Face Area of Icosidodecahedron/sqrt(3))

Circumsphere Radius of Icosidodecahedron given Volume

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

Circumsphere Radius of Icosidodecahedron given Triangular Face Height

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Height of Icosidodecahedron/sqrt(3)

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Perimeter

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Perimeter of Icosidodecahedron/10

Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter

Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6

Circumsphere Radius of Icosidodecahedron

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

Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter Formula

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6
r_c = (1+sqrt(5))*P_Triangle/6

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 Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter?

Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter calculator uses Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6 to calculate the Circumsphere Radius of Icosidodecahedron, Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the triangular face perimeter of the Icosidodecahedron. Circumsphere Radius of Icosidodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter using this online calculator? To use this online calculator for Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter, enter Triangular Face Perimeter of Icosidodecahedron (P_Triangle) and hit the calculate button. Here is how the Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter calculation can be explained with given input values -> 16.18034 = (1+sqrt(5))*30/6.

FAQ

What is Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter?

Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the triangular face perimeter of the Icosidodecahedron and is represented as r_c = (1+sqrt(5))*P_Triangle/6 or Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6. Triangular Face Perimeter of Icosidodecahedron is the total length of all the boundary lines of any of the triangular faces of the Icosidodecahedron.

How to calculate Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter?

Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the triangular face perimeter of the Icosidodecahedron is calculated using Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Perimeter of Icosidodecahedron/6. To calculate Circumsphere Radius of Icosidodecahedron given Triangular Face Perimeter, you need Triangular Face Perimeter of Icosidodecahedron (P_Triangle). With our tool, you need to enter the respective value for Triangular Face Perimeter 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 Circumsphere Radius of Icosidodecahedron?

In this formula, Circumsphere Radius of Icosidodecahedron uses Triangular Face Perimeter of Icosidodecahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*Edge Length of Icosidodecahedron
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/(sqrt(5+(2*sqrt(5))))*Midsphere Radius of Icosidodecahedron
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*(3*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5))))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*sqrt(Triangular Face Area of Icosidodecahedron/sqrt(3))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Triangular Face Height of Icosidodecahedron/sqrt(3)
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5)))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*sqrt((Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5))))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Perimeter of Icosidodecahedron/10

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