## Space Diagonal of Icosahedron given Face Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6
dSpace = sqrt(10+(2*sqrt(5)))*PFace/6
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
Space Diagonal of Icosahedron - (Measured in Meter) - The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
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.
STEP 1: Convert Input(s) to Base Unit
Face Perimeter of Icosahedron: 30 Meter --> 30 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = sqrt(10+(2*sqrt(5)))*PFace/6 --> sqrt(10+(2*sqrt(5)))*30/6
Evaluating ... ...
dSpace = 19.0211303259031
STEP 3: Convert Result to Output's Unit
19.0211303259031 Meter --> No Conversion Required
19.0211303259031 19.02113 Meter <-- Space Diagonal 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 Space Diagonal of Icosahedron Calculators

Space Diagonal of Icosahedron given Surface to Volume Ratio
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Space Diagonal of Icosahedron given Lateral Surface Area
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Space Diagonal of Icosahedron given Insphere Radius
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Space Diagonal of Icosahedron given Total Surface Area
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Space Diagonal of Icosahedron given Face Area
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Space Diagonal of Icosahedron given Volume
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
Space Diagonal of Icosahedron given Midsphere Radius
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Space Diagonal of Icosahedron given Face Perimeter
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6
Space Diagonal of Icosahedron
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron
Space Diagonal of Icosahedron given Perimeter
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/60
Space Diagonal of Icosahedron given Circumsphere Radius
Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron

## Space Diagonal of Icosahedron given Face Perimeter Formula

Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6
dSpace = sqrt(10+(2*sqrt(5)))*PFace/6

## 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 Space Diagonal of Icosahedron given Face Perimeter?

Space Diagonal of Icosahedron given Face Perimeter calculator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6 to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Face Perimeter formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the face perimeter of the Icosahedron. Space Diagonal of Icosahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Icosahedron given Face Perimeter using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Face Perimeter, enter Face Perimeter of Icosahedron (PFace) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Face Perimeter calculation can be explained with given input values -> 19.02113 = sqrt(10+(2*sqrt(5)))*30/6.

### FAQ

What is Space Diagonal of Icosahedron given Face Perimeter?
The Space Diagonal of Icosahedron given Face Perimeter formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the face perimeter of the Icosahedron and is represented as dSpace = sqrt(10+(2*sqrt(5)))*PFace/6 or Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6. Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.
How to calculate Space Diagonal of Icosahedron given Face Perimeter?
The Space Diagonal of Icosahedron given Face Perimeter formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the face perimeter of the Icosahedron is calculated using Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/6. To calculate Space Diagonal of Icosahedron given Face Perimeter, you need Face Perimeter of Icosahedron (PFace). With our tool, you need to enter the respective value for Face Perimeter 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 Space Diagonal of Icosahedron?
In this formula, Space Diagonal of Icosahedron uses Face Perimeter of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
• Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3))
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
• Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/60
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