Circumsphere Radius of Great Icosahedron given Long Ridge Length Calculator

✖Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Long Ridge Length of Great Icosahedron [l_Ridge(Long)]

+10%

-10%

✖Circumsphere Radius of Great Icosahedron is the radius of the sphere that contains the Great Icosahedron in such a way that all the peak vertices are lying on the sphere.ⓘ Circumsphere Radius of Great Icosahedron given Long Ridge Length [r_c]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Circumsphere Radius of Great Icosahedron given Long Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))
r_c = sqrt(50+(22*sqrt(5)))/4*(10*l_Ridge(Long))/(sqrt(2)*(5+(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

Circumsphere Radius of Great Icosahedron - (Measured in Meter) - Circumsphere Radius of Great Icosahedron is the radius of the sphere that contains the Great Icosahedron in such a way that all the peak vertices are lying on the sphere.
Long Ridge Length of Great Icosahedron - (Measured in Meter) - Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

STEP 1: Convert Input(s) to Base Unit

Long Ridge Length of Great Icosahedron: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(50+(22*sqrt(5)))/4*(10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))) --> sqrt(50+(22*sqrt(5)))/4*(10*17)/(sqrt(2)*(5+(3*sqrt(5))))

Evaluating ... ...

r_c = 25.5637905878207

STEP 3: Convert Result to Output's Unit

25.5637905878207 Meter --> No Conversion Required

FINAL ANSWER

25.5637905878207 ≈ 25.56379 Meter <-- Circumsphere Radius of Great Icosahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Great Icosahedron » Radius of Great Icosahedron » Circumsphere Radius of Great Icosahedron given Long Ridge Length

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< Radius of Great Icosahedron Calculators

Circumsphere Radius of Great Icosahedron given Long Ridge Length

LaTeX Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))

Circumsphere Radius of Great Icosahedron given Mid Ridge Length

LaTeX Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))

Circumsphere Radius of Great Icosahedron given Short Ridge Length

LaTeX Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Circumsphere Radius of Great Icosahedron

LaTeX Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*Edge Length of Great Icosahedron

Circumsphere Radius of Great Icosahedron given Long Ridge Length Formula

LaTeX Go

What is Great Icosahedron?

The Great Icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance phi, the golden ratio. The solid therefore consists of 20 equilateral triangles. The symmetry of their arrangement is such that the resulting solid contains 12 pentagrams.

How to Calculate Circumsphere Radius of Great Icosahedron given Long Ridge Length?

Circumsphere Radius of Great Icosahedron given Long Ridge Length calculator uses Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))) to calculate the Circumsphere Radius of Great Icosahedron, Circumsphere Radius of Great Icosahedron given Long Ridge Length formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using long ridge length. Circumsphere Radius of Great Icosahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Icosahedron given Long Ridge Length using this online calculator? To use this online calculator for Circumsphere Radius of Great Icosahedron given Long Ridge Length, enter Long Ridge Length of Great Icosahedron (l_Ridge(Long)) and hit the calculate button. Here is how the Circumsphere Radius of Great Icosahedron given Long Ridge Length calculation can be explained with given input values -> 25.56379 = sqrt(50+(22*sqrt(5)))/4*(10*17)/(sqrt(2)*(5+(3*sqrt(5)))).

FAQ

What is Circumsphere Radius of Great Icosahedron given Long Ridge Length?

Circumsphere Radius of Great Icosahedron given Long Ridge Length formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using long ridge length and is represented as r_c = sqrt(50+(22*sqrt(5)))/4*(10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))) or Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))). Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

How to calculate Circumsphere Radius of Great Icosahedron given Long Ridge Length?

Circumsphere Radius of Great Icosahedron given Long Ridge Length formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using long ridge length is calculated using Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))). To calculate Circumsphere Radius of Great Icosahedron given Long Ridge Length, you need Long Ridge Length of Great Icosahedron (l_Ridge(Long)). With our tool, you need to enter the respective value for Long Ridge Length of Great 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 Circumsphere Radius of Great Icosahedron?

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

Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*Edge Length of Great Icosahedron
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Home

FREE PDFs

🔍 Search