## Space Diagonal of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
dSpace = sqrt(10+(2*sqrt(5)))*(6*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
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.
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
dSpace = sqrt(10+(2*sqrt(5)))*(6*ri)/(sqrt(3)*(3+sqrt(5))) --> sqrt(10+(2*sqrt(5)))*(6*7)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
dSpace = 17.6177200131075
STEP 3: Convert Result to Output's Unit
17.6177200131075 Meter --> No Conversion Required
17.6177200131075 17.61772 Meter <-- Space Diagonal of Icosahedron
(Calculation completed in 00.021 seconds)
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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 Insphere Radius Formula

Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
dSpace = sqrt(10+(2*sqrt(5)))*(6*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 Space Diagonal of Icosahedron given Insphere Radius?

Space Diagonal of Icosahedron given Insphere Radius calculator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Insphere Radius calculation can be explained with given input values -> 17.61772 = sqrt(10+(2*sqrt(5)))*(6*7)/(sqrt(3)*(3+sqrt(5))).

### FAQ

What is Space Diagonal of Icosahedron given Insphere Radius?
The Space Diagonal of Icosahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the insphere radius of the Icosahedron and is represented as dSpace = sqrt(10+(2*sqrt(5)))*(6*ri)/(sqrt(3)*(3+sqrt(5))) or Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*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 Space Diagonal of Icosahedron given Insphere Radius?
The Space Diagonal of Icosahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the insphere radius of the Icosahedron is calculated using Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Space Diagonal 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 Space Diagonal of Icosahedron?
In this formula, Space Diagonal of Icosahedron uses Insphere Radius 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)))*(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((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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