## Face Perimeter of Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
PFace = (36*sqrt(3))/((3+sqrt(5))*RA/V)
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Face Perimeter of Icosahedron - (Measured in Meter) - Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.
Surface to Volume Ratio of Icosahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Icosahedron: 0.4 1 per Meter --> 0.4 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PFace = (36*sqrt(3))/((3+sqrt(5))*RA/V) --> (36*sqrt(3))/((3+sqrt(5))*0.4)
Evaluating ... ...
PFace = 29.7713042212323
STEP 3: Convert Result to Output's Unit
29.7713042212323 Meter --> No Conversion Required
29.7713042212323 29.7713 Meter <-- Face Perimeter of Icosahedron
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 11 Face Perimeter of Icosahedron Calculators

Face Perimeter of Icosahedron given Surface to Volume Ratio
Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Face Perimeter of Icosahedron given Circumsphere Radius
Face Perimeter of Icosahedron = (12*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Face Perimeter of Icosahedron given Lateral Surface Area
Face Perimeter of Icosahedron = 3*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Face Perimeter of Icosahedron given Insphere Radius
Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Face Perimeter of Icosahedron given Space Diagonal
Face Perimeter of Icosahedron = (6*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Face Perimeter of Icosahedron given Total Surface Area
Face Perimeter of Icosahedron = 3*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Face Perimeter of Icosahedron given Face Area
Face Perimeter of Icosahedron = 3*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Face Perimeter of Icosahedron given Volume
Face Perimeter of Icosahedron = 3*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Face Perimeter of Icosahedron given Midsphere Radius
Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Face Perimeter of Icosahedron
Face Perimeter of Icosahedron = 3*Edge Length of Icosahedron
Face Perimeter of Icosahedron given Perimeter
Face Perimeter of Icosahedron = Perimeter of Icosahedron/10

## Face Perimeter of Icosahedron given Surface to Volume Ratio Formula

Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
PFace = (36*sqrt(3))/((3+sqrt(5))*RA/V)

## What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Face Perimeter of Icosahedron given Surface to Volume Ratio?

Face Perimeter of Icosahedron given Surface to Volume Ratio calculator uses Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron) to calculate the Face Perimeter of Icosahedron, The Face Perimeter of Icosahedron given Surface to Volume Ratio formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the surface to volume ratio of the Icosahedron. Face Perimeter of Icosahedron is denoted by PFace symbol.

How to calculate Face Perimeter of Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Face Perimeter of Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Icosahedron (RA/V) and hit the calculate button. Here is how the Face Perimeter of Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 29.7713 = (36*sqrt(3))/((3+sqrt(5))*0.4).

### FAQ

What is Face Perimeter of Icosahedron given Surface to Volume Ratio?
The Face Perimeter of Icosahedron given Surface to Volume Ratio formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the surface to volume ratio of the Icosahedron and is represented as PFace = (36*sqrt(3))/((3+sqrt(5))*RA/V) or Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.
How to calculate Face Perimeter of Icosahedron given Surface to Volume Ratio?
The Face Perimeter of Icosahedron given Surface to Volume Ratio formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the surface to volume ratio of the Icosahedron is calculated using Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). To calculate Face Perimeter of Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Icosahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of 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 Face Perimeter of Icosahedron?
In this formula, Face Perimeter of Icosahedron uses Surface to Volume Ratio of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
• Face Perimeter of Icosahedron = 3*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
• Face Perimeter of Icosahedron = 3*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
• Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
• Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5))
• Face Perimeter of Icosahedron = (12*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
• Face Perimeter of Icosahedron = 3*Edge Length of Icosahedron
• Face Perimeter of Icosahedron = 3*sqrt((4*Face Area of Icosahedron)/sqrt(3))
• Face Perimeter of Icosahedron = (6*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
• Face Perimeter of Icosahedron = 3*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
• Face Perimeter of Icosahedron = Perimeter of Icosahedron/10
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