Face Perimeter of Icosahedron given Midsphere Radius Calculator

✖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.ⓘ Midsphere Radius of Icosahedron [r_m]

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✖Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.ⓘ Face Perimeter of Icosahedron given Midsphere Radius [P_Face]

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Formula

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Face Perimeter of Icosahedron given Midsphere Radius

Formula

`"P"_{"Face"} = (12*"r"_{"m"})/(1+sqrt(5))`

Example

`"29.66563m"=(12*"8m")/(1+sqrt(5))`

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Face Perimeter of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5))
P_Face = (12*r_m)/(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

Face Perimeter of Icosahedron - (Measured in Meter) - Face Perimeter of Icosahedron is the total distance around the five edges of any face 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_Face = (12*r_m)/(1+sqrt(5)) --> (12*8)/(1+sqrt(5))

Evaluating ... ...

P_Face = 29.665631459995

STEP 3: Convert Result to Output's Unit

29.665631459995 Meter --> No Conversion Required

FINAL ANSWER

29.665631459995 ≈ 29.66563 Meter <-- Face Perimeter of Icosahedron

(Calculation completed in 00.004 seconds)

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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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< 11 Face Perimeter of Icosahedron Calculators

Face Perimeter of Icosahedron given Surface to Volume Ratio

Go Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Face Perimeter of Icosahedron given Circumsphere Radius

Go Face Perimeter of Icosahedron = (12*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))

Face Perimeter of Icosahedron given Lateral Surface Area

Go Face Perimeter of Icosahedron = 3*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))

Face Perimeter of Icosahedron given Insphere Radius

Go Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

Face Perimeter of Icosahedron given Space Diagonal

Go Face Perimeter of Icosahedron = (6*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))

Face Perimeter of Icosahedron given Total Surface Area

Go Face Perimeter of Icosahedron = 3*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))

Face Perimeter of Icosahedron given Face Area

Go Face Perimeter of Icosahedron = 3*sqrt((4*Face Area of Icosahedron)/sqrt(3))

Face Perimeter of Icosahedron given Volume

Go Face Perimeter of Icosahedron = 3*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)

Face Perimeter of Icosahedron given Midsphere Radius

Go Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5))

Face Perimeter of Icosahedron

Go Face Perimeter of Icosahedron = 3*Edge Length of Icosahedron

Face Perimeter of Icosahedron given Perimeter

Go Face Perimeter of Icosahedron = Perimeter of Icosahedron/10

Face Perimeter of Icosahedron given Midsphere Radius Formula

Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5))
P_Face = (12*r_m)/(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 Face Perimeter of Icosahedron given Midsphere Radius?

Face Perimeter of Icosahedron given Midsphere Radius calculator uses Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5)) to calculate the Face Perimeter of Icosahedron, The Face Perimeter of Icosahedron given Midsphere Radius formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the midsphere radius of the Icosahedron. Face Perimeter of Icosahedron is denoted by P_Face symbol.

How to calculate Face Perimeter of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Face Perimeter of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (r_m) and hit the calculate button. Here is how the Face Perimeter of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 29.66563 = (12*8)/(1+sqrt(5)).

FAQ

What is Face Perimeter of Icosahedron given Midsphere Radius?

The Face Perimeter of Icosahedron given Midsphere Radius formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the midsphere radius of the Icosahedron and is represented as P_Face = (12*r_m)/(1+sqrt(5)) or Face Perimeter of Icosahedron = (12*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 Face Perimeter of Icosahedron given Midsphere Radius?

The Face Perimeter of Icosahedron given Midsphere Radius formula is defined as the total distance around the three edges of any face of the Icosahedron, and is calculated using the midsphere radius of the Icosahedron is calculated using Face Perimeter of Icosahedron = (12*Midsphere Radius of Icosahedron)/(1+sqrt(5)). To calculate Face Perimeter of Icosahedron given Midsphere Radius, you need Midsphere Radius of Icosahedron (r_m). 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 Face Perimeter of Icosahedron?

In this formula, Face Perimeter of Icosahedron uses Midsphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -

Face Perimeter of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Face Perimeter of Icosahedron = 3*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Face Perimeter of Icosahedron = 3*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Face Perimeter of Icosahedron = (36*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Face Perimeter of Icosahedron = (12*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Face Perimeter of Icosahedron = 3*Edge Length of Icosahedron
Face Perimeter of Icosahedron = 3*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Face Perimeter of Icosahedron = (6*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Face Perimeter of Icosahedron = 3*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Face Perimeter of Icosahedron = Perimeter of Icosahedron/10

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