Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length Calculator

✖Icosahedral Edge Length of Truncated Icosahedron is the length of any edge of the larger Icosahedron from which the corners are cut to form the Truncated Icosahedron.ⓘ Icosahedral Edge Length of Truncated Icosahedron [l_{e(Icosahedron)}]

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✖Midsphere Radius of Truncated Icosahedron is the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length [r_m]

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Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
r_m = (1+sqrt(5))/4*l_{e(Icosahedron)}
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 Truncated Icosahedron - (Measured in Meter) - Midsphere Radius of Truncated Icosahedron is the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere.
Icosahedral Edge Length of Truncated Icosahedron - (Measured in Meter) - Icosahedral Edge Length of Truncated Icosahedron is the length of any edge of the larger Icosahedron from which the corners are cut to form the Truncated Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Icosahedral Edge Length of Truncated Icosahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (1+sqrt(5))/4*l_{e(Icosahedron)} --> (1+sqrt(5))/4*30

Evaluating ... ...

r_m = 24.2705098312484

STEP 3: Convert Result to Output's Unit

24.2705098312484 Meter --> No Conversion Required

FINAL ANSWER

24.2705098312484 ≈ 24.27051 Meter <-- Midsphere Radius of Truncated Icosahedron

(Calculation completed in 00.020 seconds)

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< Midsphere Radius of Truncated Icosahedron Calculators

Midsphere Radius of Truncated Icosahedron given Total Surface Area

LaTeX Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))

Midsphere Radius of Truncated Icosahedron given Volume

LaTeX Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)

Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length

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

Midsphere Radius of Truncated Icosahedron

LaTeX Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron

< Important Formulas of Truncated Icosahedron Calculators

Edge Length of Truncated Icosahedron given Circumsphere Radius

LaTeX Go Edge Length of Truncated Icosahedron = (4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5))))

Edge Length of Truncated Icosahedron given Volume

LaTeX Go Edge Length of Truncated Icosahedron = ((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)

Edge Length of Truncated Icosahedron given Midsphere Radius

LaTeX Go Edge Length of Truncated Icosahedron = (4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5)))

Icosahedral Edge Length of Truncated Icosahedron

LaTeX Go Icosahedral Edge Length of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron

Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length Formula

LaTeX Go

Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
r_m = (1+sqrt(5))/4*l_{e(Icosahedron)}

What is Truncated Icosahedron and its applications?

In geometry, the Truncated Icosahedron is an Archimedean solid, one of 13 convex isogonal non-prismatic solids whose faces are two or more types of regular polygons. It has a total of 32 faces which include 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is used in the cell-transitive hyperbolic space-filling tessellation, the bi-truncated order-5 dodecahedral honeycomb.

How to Calculate Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length?

Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length calculator uses Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron to calculate the Midsphere Radius of Truncated Icosahedron, Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere, and calculated using the icosahedral edge length of the Truncated Icosahedron. Midsphere Radius of Truncated Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length using this online calculator? To use this online calculator for Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length, enter Icosahedral Edge Length of Truncated Icosahedron (l_{e(Icosahedron)}) and hit the calculate button. Here is how the Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length calculation can be explained with given input values -> 24.27051 = (1+sqrt(5))/4*30.

FAQ

What is Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length?

Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere, and calculated using the icosahedral edge length of the Truncated Icosahedron and is represented as r_m = (1+sqrt(5))/4*l_{e(Icosahedron)} or Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron. Icosahedral Edge Length of Truncated Icosahedron is the length of any edge of the larger Icosahedron from which the corners are cut to form the Truncated Icosahedron.

How to calculate Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length?

Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere, and calculated using the icosahedral edge length of the Truncated Icosahedron is calculated using Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron. To calculate Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length, you need Icosahedral Edge Length of Truncated Icosahedron (l_{e(Icosahedron)}). With our tool, you need to enter the respective value for Icosahedral Edge Length of Truncated 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 Truncated Icosahedron?

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

Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)

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