Insphere Radius of Icosahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5)))
ri = (sqrt(3)*(3+sqrt(5)))/12*(2*dSpace)/sqrt(10+(2*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
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.
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
ri = (sqrt(3)*(3+sqrt(5)))/12*(2*dSpace)/sqrt(10+(2*sqrt(5))) --> (sqrt(3)*(3+sqrt(5)))/12*(2*19)/sqrt(10+(2*sqrt(5)))
Evaluating ... ...
ri = 7.54921748677178
STEP 3: Convert Result to Output's Unit
7.54921748677178 Meter --> No Conversion Required
FINAL ANSWER
7.54921748677178 7.549217 Meter <-- Insphere Radius of Icosahedron
(Calculation completed in 00.020 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 Insphere Radius of Icosahedron Calculators

Insphere Radius of Icosahedron given Surface to Volume Ratio
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Insphere Radius of Icosahedron given Circumsphere Radius
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Circumsphere Radius of Icosahedron)/sqrt(10+(2*sqrt(5)))
Insphere Radius of Icosahedron given Lateral Surface Area
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Insphere Radius of Icosahedron given Space Diagonal
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5)))
Insphere Radius of Icosahedron given Total Surface Area
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Insphere Radius of Icosahedron given Face Area
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Insphere Radius of Icosahedron given Volume
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Insphere Radius of Icosahedron given Midsphere Radius
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Insphere Radius of Icosahedron given Face Perimeter
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36
Insphere Radius of Icosahedron
​ Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
Insphere Radius of Icosahedron given Perimeter
​ Go Insphere Radius of Icosahedron = sqrt(3)*(3+sqrt(5))*Perimeter of Icosahedron/360

Insphere Radius of Icosahedron given Space Diagonal Formula

Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5)))
ri = (sqrt(3)*(3+sqrt(5)))/12*(2*dSpace)/sqrt(10+(2*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 Insphere Radius of Icosahedron given Space Diagonal?

Insphere Radius of Icosahedron given Space Diagonal calculator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))) to calculate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the space diagonal of the Icosahedron. Insphere Radius of Icosahedron is denoted by ri symbol.

How to calculate Insphere Radius of Icosahedron given Space Diagonal using this online calculator? To use this online calculator for Insphere Radius of Icosahedron given Space Diagonal, enter Space Diagonal of Icosahedron (dSpace) and hit the calculate button. Here is how the Insphere Radius of Icosahedron given Space Diagonal calculation can be explained with given input values -> 7.549217 = (sqrt(3)*(3+sqrt(5)))/12*(2*19)/sqrt(10+(2*sqrt(5))).

FAQ

What is Insphere Radius of Icosahedron given Space Diagonal?
The Insphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the space diagonal of the Icosahedron and is represented as ri = (sqrt(3)*(3+sqrt(5)))/12*(2*dSpace)/sqrt(10+(2*sqrt(5))) or Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))). The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
How to calculate Insphere Radius of Icosahedron given Space Diagonal?
The Insphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the space diagonal of the Icosahedron is calculated using Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))). To calculate Insphere 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 Insphere Radius of Icosahedron?
In this formula, Insphere Radius of Icosahedron uses Space Diagonal of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Circumsphere Radius of Icosahedron)/sqrt(10+(2*sqrt(5)))
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Insphere Radius of Icosahedron = sqrt(3)*(3+sqrt(5))*Perimeter of Icosahedron/360
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