Edge Length of Great Icosahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.ⓘ Surface to Volume Ratio of Great Icosahedron [R_A/V]

+10%

-10%

✖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 Surface to Volume Ratio [l_e]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Edge Length of Great Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)
l_e = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V)
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.
Surface to Volume Ratio of Great Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Icosahedron: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V) --> (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6)

Evaluating ... ...

l_e = 10.7046626931927

STEP 3: Convert Result to Output's Unit

10.7046626931927 Meter --> No Conversion Required

FINAL ANSWER

10.7046626931927 ≈ 10.70466 Meter <-- Edge Length of Great Icosahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Great Icosahedron » Edge Length of Great Icosahedron » Edge Length of Great Icosahedron given Surface to Volume Ratio

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 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 Surface to Volume Ratio Formula

LaTeX Go

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

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 Surface to Volume Ratio?

Edge Length of Great Icosahedron given Surface to Volume Ratio calculator uses Edge Length of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron) to calculate the Edge Length of Great Icosahedron, Edge Length of Great Icosahedron given Surface to Volume Ratio 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 surface to volume ratio. Edge Length of Great Icosahedron is denoted by l_e symbol.

How to calculate Edge Length of Great Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Great Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Icosahedron (R_A/V) and hit the calculate button. Here is how the Edge Length of Great Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 10.70466 = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6).

FAQ

What is Edge Length of Great Icosahedron given Surface to Volume Ratio?

Edge Length of Great Icosahedron given Surface to Volume Ratio 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 surface to volume ratio and is represented as l_e = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V) or Edge Length of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron). Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

How to calculate Edge Length of Great Icosahedron given Surface to Volume Ratio?

Edge Length of Great Icosahedron given Surface to Volume Ratio 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 surface to volume ratio is calculated using Edge Length of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron). To calculate Edge Length of Great Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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)

Home

FREE PDFs

🔍 Search