Long Ridge Length of Great Icosahedron given Mid Ridge Length Calculator

✖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 [l_Ridge(Mid)]

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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 Mid Ridge Length [l_Ridge(Long)]

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Long Ridge Length of Great Icosahedron given Mid Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

Mid Ridge Length of Great Icosahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*l_Ridge(Mid))/(1+sqrt(5)) --> (sqrt(2)*(5+(3*sqrt(5))))/10*(2*16)/(1+sqrt(5))

Evaluating ... ...

l_Ridge(Long) = 16.3733527552542

STEP 3: Convert Result to Output's Unit

16.3733527552542 Meter --> No Conversion Required

FINAL ANSWER

16.3733527552542 ≈ 16.37335 Meter <-- Long Ridge Length of Great Icosahedron

(Calculation completed in 00.020 seconds)

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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 Mid Ridge Length Formula

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

Long Ridge Length of Great Icosahedron given Mid Ridge Length calculator uses Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)) to calculate the Long Ridge Length of Great Icosahedron, Long Ridge Length of Great Icosahedron given Mid 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 long 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 Mid Ridge Length using this online calculator? To use this online calculator for Long Ridge Length of Great Icosahedron given Mid Ridge Length, enter Mid Ridge Length of Great Icosahedron (l_Ridge(Mid)) and hit the calculate button. Here is how the Long Ridge Length of Great Icosahedron given Mid Ridge Length calculation can be explained with given input values -> 16.37335 = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*16)/(1+sqrt(5)).

FAQ

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

Long Ridge Length of Great Icosahedron given Mid 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 long ridge length and is represented as l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*l_Ridge(Mid))/(1+sqrt(5)) or Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)). 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.

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

Long Ridge Length of Great Icosahedron given Mid 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 long ridge length is calculated using Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)). To calculate Long Ridge Length of Great Icosahedron given Mid Ridge Length, you need Mid Ridge Length of Great Icosahedron (l_Ridge(Mid)). With our tool, you need to enter the respective value for Mid 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 Mid 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*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
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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