## Space Diagonal of Icosahedron given Face Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3))
dSpace = sqrt(10+(2*sqrt(5)))/2*sqrt((4*AFace)/sqrt(3))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, 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 Area of Icosahedron - (Measured in Square Meter) - The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Face Area of Icosahedron: 45 Square Meter --> 45 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = sqrt(10+(2*sqrt(5)))/2*sqrt((4*AFace)/sqrt(3)) --> sqrt(10+(2*sqrt(5)))/2*sqrt((4*45)/sqrt(3))
Evaluating ... ...
dSpace = 19.3906452064276
STEP 3: Convert Result to Output's Unit
19.3906452064276 Meter --> No Conversion Required
19.3906452064276 19.39065 Meter <-- Space Diagonal of Icosahedron
(Calculation completed in 00.003 seconds)
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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 Area Formula

Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3))
dSpace = sqrt(10+(2*sqrt(5)))/2*sqrt((4*AFace)/sqrt(3))

## 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 Area?

Space Diagonal of Icosahedron given Face Area calculator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Face Area 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 area of the Icosahedron. Space Diagonal of Icosahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Icosahedron given Face Area using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Face Area, enter Face Area of Icosahedron (AFace) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Face Area calculation can be explained with given input values -> 19.39065 = sqrt(10+(2*sqrt(5)))/2*sqrt((4*45)/sqrt(3)).

### FAQ

What is Space Diagonal of Icosahedron given Face Area?
The Space Diagonal of Icosahedron given Face Area 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 area of the Icosahedron and is represented as dSpace = sqrt(10+(2*sqrt(5)))/2*sqrt((4*AFace)/sqrt(3)) or Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)). The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
How to calculate Space Diagonal of Icosahedron given Face Area?
The Space Diagonal of Icosahedron given Face Area 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 area of the Icosahedron is calculated using Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)). To calculate Space Diagonal of Icosahedron given Face Area, you need Face Area of Icosahedron (AFace). With our tool, you need to enter the respective value for Face Area 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 Area 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)))*Face Perimeter of Icosahedron/6
• 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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