Mid Ridge Length of Great Icosahedron given Circumsphere Radius Calculator

✖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 [r_c]

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✖Mid Ridge Length of Great Icosahedron the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Mid Ridge Length of Great Icosahedron given Circumsphere Radius [l_Ridge(Mid)]

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Mid Ridge Length of Great Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Mid Ridge Length of Great Icosahedron - (Measured in Meter) - Mid Ridge Length of Great Icosahedron the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached.
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.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Great Icosahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Ridge(Mid) = (1+sqrt(5))/2*(4*r_c)/sqrt(50+(22*sqrt(5))) --> (1+sqrt(5))/2*(4*25)/sqrt(50+(22*sqrt(5)))

Evaluating ... ...

l_Ridge(Mid) = 16.2459848116453

STEP 3: Convert Result to Output's Unit

16.2459848116453 Meter --> No Conversion Required

FINAL ANSWER

16.2459848116453 ≈ 16.24598 Meter <-- Mid Ridge Length of Great Icosahedron

(Calculation completed in 00.013 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Mid Ridge Length of Great Icosahedron Calculators

Mid Ridge Length of Great Icosahedron given Long Ridge Length

LaTeX Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))

Mid Ridge Length of Great Icosahedron given Circumsphere Radius

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

Mid Ridge Length of Great Icosahedron given Short Ridge Length

LaTeX Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Mid Ridge Length of Great Icosahedron

LaTeX Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*Edge Length of Great Icosahedron

Mid Ridge Length of Great Icosahedron given Circumsphere Radius Formula

LaTeX Go

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

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 Mid Ridge Length of Great Icosahedron given Circumsphere Radius?

Mid Ridge Length of Great Icosahedron given Circumsphere Radius calculator uses Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(4*Circumsphere Radius of Great Icosahedron)/sqrt(50+(22*sqrt(5))) to calculate the Mid Ridge Length of Great Icosahedron, Mid Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using circumsphere radius. Mid Ridge Length of Great Icosahedron is denoted by l_Ridge(Mid) symbol.

How to calculate Mid Ridge Length of Great Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Mid Ridge Length of Great Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Great Icosahedron (r_c) and hit the calculate button. Here is how the Mid Ridge Length of Great Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 16.24598 = (1+sqrt(5))/2*(4*25)/sqrt(50+(22*sqrt(5))).

FAQ

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

Mid Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using circumsphere radius and is represented as l_Ridge(Mid) = (1+sqrt(5))/2*(4*r_c)/sqrt(50+(22*sqrt(5))) or Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(4*Circumsphere Radius of Great Icosahedron)/sqrt(50+(22*sqrt(5))). 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.

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

Mid Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using circumsphere radius is calculated using Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(4*Circumsphere Radius of Great Icosahedron)/sqrt(50+(22*sqrt(5))). To calculate Mid Ridge Length of Great Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Great Icosahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Mid Ridge Length of Great Icosahedron?

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

Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*Edge Length of Great Icosahedron
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

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