Perimeter of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5))
P = (120*rm)/(1+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
Perimeter of Icosahedron - (Measured in Meter) - Perimeter of Icosahedron is the sum of the total distance around all the edges of the 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
P = (120*rm)/(1+sqrt(5)) --> (120*8)/(1+sqrt(5))
Evaluating ... ...
P = 296.656314599949
STEP 3: Convert Result to Output's Unit
296.656314599949 Meter --> No Conversion Required
FINAL ANSWER
296.656314599949 296.6563 Meter <-- Perimeter of Icosahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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11 Perimeter of Icosahedron Calculators

Perimeter of Icosahedron given Surface to Volume Ratio
Go Perimeter of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Perimeter of Icosahedron given Circumsphere Radius
Go Perimeter of Icosahedron = (120*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Perimeter of Icosahedron given Lateral Surface Area
Go Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Perimeter of Icosahedron given Insphere Radius
Go Perimeter of Icosahedron = (360*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Perimeter of Icosahedron given Space Diagonal
Go Perimeter of Icosahedron = (60*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Perimeter of Icosahedron given Total Surface Area
Go Perimeter of Icosahedron = 30*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Perimeter of Icosahedron given Face Area
Go Perimeter of Icosahedron = 30*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Perimeter of Icosahedron given Volume
Go Face Perimeter of Icosahedron = 30*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Perimeter of Icosahedron given Midsphere Radius
Go Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Perimeter of Icosahedron given Face Perimeter
Go Perimeter of Icosahedron = 10*Face Perimeter of Icosahedron
Perimeter of Icosahedron
Go Perimeter of Icosahedron = 30*Edge Length of Icosahedron

Perimeter of Icosahedron given Midsphere Radius Formula

Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5))
P = (120*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 Perimeter of Icosahedron given Midsphere Radius?

Perimeter of Icosahedron given Midsphere Radius calculator uses Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5)) to calculate the Perimeter of Icosahedron, The Perimeter of Icosahedron given Midsphere Radius formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the midsphere radius of the Icosahedron. Perimeter of Icosahedron is denoted by P symbol.

How to calculate Perimeter of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Perimeter of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (rm) and hit the calculate button. Here is how the Perimeter of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 296.6563 = (120*8)/(1+sqrt(5)).

FAQ

What is Perimeter of Icosahedron given Midsphere Radius?
The Perimeter of Icosahedron given Midsphere Radius formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the midsphere radius of the Icosahedron and is represented as P = (120*rm)/(1+sqrt(5)) or Perimeter of Icosahedron = (120*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 Perimeter of Icosahedron given Midsphere Radius?
The Perimeter of Icosahedron given Midsphere Radius formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the midsphere radius of the Icosahedron is calculated using Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5)). To calculate Perimeter 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 Perimeter of Icosahedron?
In this formula, Perimeter of Icosahedron uses Midsphere Radius of Icosahedron. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Perimeter of Icosahedron = 30*Edge Length of Icosahedron
  • Perimeter of Icosahedron = (120*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Perimeter of Icosahedron = 30*sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Perimeter of Icosahedron = (360*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
  • Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Perimeter of Icosahedron = 10*Face Perimeter of Icosahedron
  • Perimeter of Icosahedron = (60*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Perimeter of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Perimeter of Icosahedron = 30*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
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