Long 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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✖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 given Circumsphere Radius [l_Ridge(Long)]

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Formula

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Long Ridge Length of Great Icosahedron given Circumsphere Radius

Formula

`"l"_{"Ridge(Long)"} = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*"r"_{"c"})/(sqrt(50+(22*sqrt(5))))`

Example

`"16.62508m"=(sqrt(2)*(5+(3*sqrt(5))))/10*(4*"25m")/(sqrt(50+(22*sqrt(5))))`

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Long Ridge Length of Great Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*r_c)/(sqrt(50+(22*sqrt(5)))) --> (sqrt(2)*(5+(3*sqrt(5))))/10*(4*25)/(sqrt(50+(22*sqrt(5))))

Evaluating ... ...

l_Ridge(Long) = 16.6250775110981

STEP 3: Convert Result to Output's Unit

16.6250775110981 Meter --> No Conversion Required

FINAL ANSWER

16.6250775110981 ≈ 16.62508 Meter <-- Long Ridge Length of Great Icosahedron

(Calculation completed in 00.004 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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< 7 Long Ridge Length of Great Icosahedron Calculators

Long Ridge Length of Great Icosahedron given Surface to Volume Ratio

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

Long Ridge Length of Great Icosahedron given Total Surface Area

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))

Long Ridge Length of Great Icosahedron given Circumsphere Radius

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

Long Ridge Length of Great Icosahedron given Volume

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)

Long Ridge Length of Great Icosahedron given Mid Ridge Length

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

Long Ridge Length of Great Icosahedron given Short Ridge Length

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

Long Ridge Length of Great Icosahedron

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

Long Ridge Length of Great Icosahedron given Circumsphere Radius Formula

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 Long Ridge Length of Great Icosahedron given Circumsphere Radius?

Long Ridge Length of Great Icosahedron given Circumsphere Radius calculator uses Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))) to calculate the Long Ridge Length of Great Icosahedron, Long Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using circumsphere radius. Long Ridge Length of Great Icosahedron is denoted by l_Ridge(Long) symbol.

How to calculate Long Ridge Length of Great Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Long 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 Long Ridge Length of Great Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 16.62508 = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*25)/(sqrt(50+(22*sqrt(5)))).

FAQ

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

Long Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using circumsphere radius and is represented as l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*r_c)/(sqrt(50+(22*sqrt(5)))) or Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(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 Long Ridge Length of Great Icosahedron given Circumsphere Radius?

Long Ridge Length of Great Icosahedron given Circumsphere Radius formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using circumsphere radius is calculated using Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))). To calculate Long 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 Long Ridge Length of Great Icosahedron?

In this formula, Long Ridge Length of Great Icosahedron uses Circumsphere Radius of Great Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*Edge Length of Great Icosahedron
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

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