Edge Length of Great Icosahedron given Volume Calculator

✖Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.ⓘ Volume of Great Icosahedron [V]

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✖Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron.ⓘ Edge Length of Great Icosahedron given Volume [l_e]

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Edge Length of Great Icosahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Great Icosahedron = ((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
l_e = ((4*V)/(25+(9*sqrt(5))))^(1/3)
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

Edge Length of Great Icosahedron - (Measured in Meter) - Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron.
Volume of Great Icosahedron - (Measured in Cubic Meter) - Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Great Icosahedron: 11000 Cubic Meter --> 11000 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = ((4*V)/(25+(9*sqrt(5))))^(1/3) --> ((4*11000)/(25+(9*sqrt(5))))^(1/3)

Evaluating ... ...

l_e = 9.91622561335221

STEP 3: Convert Result to Output's Unit

9.91622561335221 Meter --> No Conversion Required

FINAL ANSWER

9.91622561335221 ≈ 9.916226 Meter <-- Edge 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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St Joseph's College (SJC), Bengaluru

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< Edge Length of Great Icosahedron Calculators

Edge Length of Great Icosahedron given Long Ridge Length

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

Edge Length of Great Icosahedron given Circumsphere Radius

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

Edge Length of Great Icosahedron given Mid Ridge Length

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

Edge Length of Great Icosahedron given Short Ridge Length

LaTeX Go Edge Length of Great Icosahedron = (5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Edge Length of Great Icosahedron given Volume Formula

LaTeX Go

Edge Length of Great Icosahedron = ((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
l_e = ((4*V)/(25+(9*sqrt(5))))^(1/3)

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 Edge Length of Great Icosahedron given Volume?

Edge Length of Great Icosahedron given Volume calculator uses Edge Length of Great Icosahedron = ((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3) to calculate the Edge Length of Great Icosahedron, Edge Length of Great Icosahedron given Volume formula is defined as the length of any of the edges of a Great Icosahedron or the distance between any pair of adjacent vertices of the Great Icosahedron, calculated using volume. Edge Length of Great Icosahedron is denoted by l_e symbol.

How to calculate Edge Length of Great Icosahedron given Volume using this online calculator? To use this online calculator for Edge Length of Great Icosahedron given Volume, enter Volume of Great Icosahedron (V) and hit the calculate button. Here is how the Edge Length of Great Icosahedron given Volume calculation can be explained with given input values -> 9.916226 = ((4*11000)/(25+(9*sqrt(5))))^(1/3).

FAQ

What is Edge Length of Great Icosahedron given Volume?

Edge Length of Great Icosahedron given Volume formula is defined as the length of any of the edges of a Great Icosahedron or the distance between any pair of adjacent vertices of the Great Icosahedron, calculated using volume and is represented as l_e = ((4*V)/(25+(9*sqrt(5))))^(1/3) or Edge Length of Great Icosahedron = ((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3). Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.

How to calculate Edge Length of Great Icosahedron given Volume?

Edge Length of Great Icosahedron given Volume formula is defined as the length of any of the edges of a Great Icosahedron or the distance between any pair of adjacent vertices of the Great Icosahedron, calculated using volume is calculated using Edge Length of Great Icosahedron = ((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3). To calculate Edge Length of Great Icosahedron given Volume, you need Volume of Great Icosahedron (V). With our tool, you need to enter the respective value for Volume 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 Edge Length of Great Icosahedron?

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

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

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