Midsphere Radius of Icosahedron given Face Perimeter Calculator

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

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✖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 given Face Perimeter [r_m]

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Midsphere Radius of Icosahedron given Face Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Face Perimeter of Icosahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (1+sqrt(5))*P_Face/12 --> (1+sqrt(5))*30/12

Evaluating ... ...

r_m = 8.09016994374947

STEP 3: Convert Result to Output's Unit

8.09016994374947 Meter --> No Conversion Required

FINAL ANSWER

8.09016994374947 ≈ 8.09017 Meter <-- Midsphere Radius of Icosahedron

(Calculation completed in 00.020 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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Mumbai University (DJSCE), Mumbai

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< Midsphere Radius of Icosahedron Calculators

Midsphere Radius of Icosahedron given Circumsphere Radius

LaTeX Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))

Midsphere Radius of Icosahedron given Insphere Radius

LaTeX Go Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

Midsphere Radius of Icosahedron given Space Diagonal

LaTeX Go Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))

Midsphere Radius of Icosahedron

LaTeX Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron

Midsphere Radius of Icosahedron given Face Perimeter Formula

LaTeX Go

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

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 Midsphere Radius of Icosahedron given Face Perimeter?

Midsphere Radius of Icosahedron given Face Perimeter calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12 to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Face Perimeter formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face perimeter of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Icosahedron given Face Perimeter using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Face Perimeter, enter Face Perimeter of Icosahedron (P_Face) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Face Perimeter calculation can be explained with given input values -> 8.09017 = (1+sqrt(5))*30/12.

FAQ

What is Midsphere Radius of Icosahedron given Face Perimeter?

The Midsphere Radius of Icosahedron given Face Perimeter formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face perimeter of the Icosahedron and is represented as r_m = (1+sqrt(5))*P_Face/12 or Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12. Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

How to calculate Midsphere Radius of Icosahedron given Face Perimeter?

The Midsphere Radius of Icosahedron given Face Perimeter formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face perimeter of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12. To calculate Midsphere Radius of Icosahedron given Face Perimeter, you need Face Perimeter of Icosahedron (P_Face). With our tool, you need to enter the respective value for Face Perimeter 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 Midsphere Radius of Icosahedron?

In this formula, Midsphere Radius of Icosahedron uses Face Perimeter of Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron
Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

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