Space Diagonal of Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron
dSpace = 2*rc
This formula uses 2 Variables
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.
Circumsphere Radius of Icosahedron - (Measured in Meter) - Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Icosahedron: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = 2*rc --> 2*9
Evaluating ... ...
dSpace = 18
STEP 3: Convert Result to Output's Unit
18 Meter --> No Conversion Required
FINAL ANSWER
18 Meter <-- Space Diagonal of Icosahedron
(Calculation completed in 00.004 seconds)

Credits

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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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Verified by Nayana Phulphagar
Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
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11 Space Diagonal of Icosahedron Calculators

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

Space Diagonal of Icosahedron given Circumsphere Radius Formula

Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron
dSpace = 2*rc

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 Circumsphere Radius?

Space Diagonal of Icosahedron given Circumsphere Radius calculator uses Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Icosahedron (rc) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 18 = 2*9.

FAQ

What is Space Diagonal of Icosahedron given Circumsphere Radius?
The Space Diagonal of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron and is represented as dSpace = 2*rc or Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron. Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
How to calculate Space Diagonal of Icosahedron given Circumsphere Radius?
The Space Diagonal of Icosahedron given Circumsphere 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 circumsphere radius of the Icosahedron is calculated using Space Diagonal of Icosahedron = 2*Circumsphere Radius of Icosahedron. To calculate Space Diagonal of Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Icosahedron (rc). With our tool, you need to enter the respective value for Circumsphere 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 Circumsphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • 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((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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