## Space Diagonal of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))
dSpace = sqrt(10+(2*sqrt(5)))*(2*rm)/(1+sqrt(5))
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.
Midsphere Radius of Icosahedron - (Measured in Meter) - The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Icosahedron: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = sqrt(10+(2*sqrt(5)))*(2*rm)/(1+sqrt(5)) --> sqrt(10+(2*sqrt(5)))*(2*8)/(1+sqrt(5))
Evaluating ... ...
dSpace = 18.8091280733591
STEP 3: Convert Result to Output's Unit
18.8091280733591 Meter --> No Conversion Required
18.8091280733591 18.80913 Meter <-- Space Diagonal of Icosahedron
(Calculation completed in 00.004 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 Midsphere Radius Formula

Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))
dSpace = sqrt(10+(2*sqrt(5)))*(2*rm)/(1+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 Midsphere Radius?

Space Diagonal of Icosahedron given Midsphere Radius calculator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)) to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (rm) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 18.80913 = sqrt(10+(2*sqrt(5)))*(2*8)/(1+sqrt(5)).

### FAQ

What is Space Diagonal of Icosahedron given Midsphere Radius?
The Space Diagonal of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron and is represented as dSpace = sqrt(10+(2*sqrt(5)))*(2*rm)/(1+sqrt(5)) or Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)). The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.
How to calculate Space Diagonal of Icosahedron given Midsphere Radius?
The Space Diagonal of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron is calculated using Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)). To calculate Space Diagonal of Icosahedron given Midsphere Radius, you need Midsphere Radius of Icosahedron (rm). With our tool, you need to enter the respective value for Midsphere 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 Midsphere 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)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+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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