Long Ridge Length of Great Icosahedron given Short Ridge Length Calculator

✖Short Ridge Length of Great Icosahedron is defined as the maximum vertical distance between the finished bottom level and the finished top height directly above of Great Icosahedron.ⓘ Short Ridge Length of Great Icosahedron [l_Ridge(Short)]

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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 Short Ridge Length [l_Ridge(Long)]

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Long Ridge Length of Great Icosahedron given Short Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*l_Ridge(Short))/sqrt(10)
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.
Short Ridge Length of Great Icosahedron - (Measured in Meter) - Short Ridge Length of Great Icosahedron is defined as the maximum vertical distance between the finished bottom level and the finished top height directly above of Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Short Ridge Length of Great Icosahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*l_Ridge(Short))/sqrt(10) --> (sqrt(2)*(5+(3*sqrt(5))))/10*(5*6)/sqrt(10)

Evaluating ... ...

l_Ridge(Long) = 15.7082039324994

STEP 3: Convert Result to Output's Unit

15.7082039324994 Meter --> No Conversion Required

FINAL ANSWER

15.7082039324994 ≈ 15.7082 Meter <-- Long Ridge Length of Great Icosahedron

(Calculation completed in 00.006 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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< Long Ridge Length of Great Icosahedron Calculators

Long Ridge Length of Great Icosahedron given Circumsphere Radius

LaTeX 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 Mid Ridge Length

LaTeX 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

LaTeX 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

LaTeX 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 Short Ridge Length Formula

LaTeX Go

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

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 Short Ridge Length?

Long Ridge Length of Great Icosahedron given Short Ridge Length calculator uses Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10) to calculate the Long Ridge Length of Great Icosahedron, Long Ridge Length of Great Icosahedron given Short Ridge Length 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 short ridge length. Long Ridge Length of Great Icosahedron is denoted by l_Ridge(Long) symbol.

How to calculate Long Ridge Length of Great Icosahedron given Short Ridge Length using this online calculator? To use this online calculator for Long Ridge Length of Great Icosahedron given Short Ridge Length, enter Short Ridge Length of Great Icosahedron (l_Ridge(Short)) and hit the calculate button. Here is how the Long Ridge Length of Great Icosahedron given Short Ridge Length calculation can be explained with given input values -> 15.7082 = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*6)/sqrt(10).

FAQ

What is Long Ridge Length of Great Icosahedron given Short Ridge Length?

Long Ridge Length of Great Icosahedron given Short Ridge Length 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 short ridge length and is represented as l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*l_Ridge(Short))/sqrt(10) or Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10). Short Ridge Length of Great Icosahedron is defined as the maximum vertical distance between the finished bottom level and the finished top height directly above of Great Icosahedron.

How to calculate Long Ridge Length of Great Icosahedron given Short Ridge Length?

Long Ridge Length of Great Icosahedron given Short Ridge Length 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 short ridge length is calculated using Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10). To calculate Long Ridge Length of Great Icosahedron given Short Ridge Length, you need Short Ridge Length of Great Icosahedron (l_Ridge(Short)). With our tool, you need to enter the respective value for Short 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 Long Ridge Length of Great Icosahedron?

In this formula, Long Ridge Length of Great Icosahedron uses Short Ridge Length of Great Icosahedron. We can use 3 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*(4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5))))

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