Circumsphere Radius of Icosahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2
rc = dSpace/2
This formula uses 2 Variables
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Icosahedron: 19 Meter --> 19 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = dSpace/2 --> 19/2
Evaluating ... ...
rc = 9.5
STEP 3: Convert Result to Output's Unit
9.5 Meter --> No Conversion Required
FINAL ANSWER
9.5 Meter <-- Circumsphere Radius 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 Circumsphere Radius of Icosahedron Calculators

Circumsphere Radius of Icosahedron given Surface to Volume Ratio
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Circumsphere Radius of Icosahedron given Lateral Surface Area
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Circumsphere Radius of Icosahedron given Insphere Radius
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Circumsphere Radius of Icosahedron given Total Surface Area
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Circumsphere Radius of Icosahedron given Face Area
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Circumsphere Radius of Icosahedron given Volume
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Circumsphere Radius of Icosahedron given Midsphere Radius
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Circumsphere Radius of Icosahedron given Face Perimeter
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
Circumsphere Radius of Icosahedron given Perimeter
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120
Circumsphere Radius of Icosahedron
​ Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
Circumsphere Radius of Icosahedron given Space Diagonal
​ Go Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2

Circumsphere Radius of Icosahedron given Space Diagonal Formula

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

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 Circumsphere Radius of Icosahedron given Space Diagonal?

Circumsphere Radius of Icosahedron given Space Diagonal calculator uses Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2 to calculate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the space diagonal of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Icosahedron given Space Diagonal using this online calculator? To use this online calculator for Circumsphere Radius of Icosahedron given Space Diagonal, enter Space Diagonal of Icosahedron (dSpace) and hit the calculate button. Here is how the Circumsphere Radius of Icosahedron given Space Diagonal calculation can be explained with given input values -> 9.5 = 19/2.

FAQ

What is Circumsphere Radius of Icosahedron given Space Diagonal?
The Circumsphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the space diagonal of the Icosahedron and is represented as rc = dSpace/2 or Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2. The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
How to calculate Circumsphere Radius of Icosahedron given Space Diagonal?
The Circumsphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the space diagonal of the Icosahedron is calculated using Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2. To calculate Circumsphere Radius of Icosahedron given Space Diagonal, you need Space Diagonal of Icosahedron (dSpace). With our tool, you need to enter the respective value for Space Diagonal 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 Circumsphere Radius of Icosahedron?
In this formula, Circumsphere Radius of Icosahedron uses Space Diagonal of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120
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