## Face Perimeter of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
PFace = (36*ri)/(sqrt(3)*(3+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
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.
Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Icosahedron: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PFace = (36*ri)/(sqrt(3)*(3+sqrt(5))) --> (36*7)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
PFace = 27.7865506064835
STEP 3: Convert Result to Output's Unit
27.7865506064835 Meter --> No Conversion Required
27.7865506064835 27.78655 Meter <-- Face Perimeter of Icosahedron
(Calculation completed in 00.004 seconds)
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## Credits

Created by Dhruv Walia
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 Insphere Radius Formula

Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
PFace = (36*ri)/(sqrt(3)*(3+sqrt(5)))

## 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 Insphere Radius?

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

How to calculate Face Perimeter of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Face Perimeter of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Face Perimeter of Icosahedron given Insphere Radius calculation can be explained with given input values -> 27.78655 = (36*7)/(sqrt(3)*(3+sqrt(5))).

### FAQ

What is Face Perimeter of Icosahedron given Insphere Radius?
The Face Perimeter of Icosahedron given Insphere Radius formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the insphere radius of the Icosahedron and is represented as PFace = (36*ri)/(sqrt(3)*(3+sqrt(5))) or Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
How to calculate Face Perimeter of Icosahedron given Insphere Radius?
The Face Perimeter of Icosahedron given Insphere Radius formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the insphere radius of the Icosahedron is calculated using Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Face Perimeter of Icosahedron given Insphere Radius, you need Insphere Radius of Icosahedron (ri). With our tool, you need to enter the respective value for Insphere Radius 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 Insphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
• Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
• 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 = (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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