Midsphere Radius of Truncated Icosahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron
rm = (3*(1+sqrt(5)))/4*le
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.
Edge Length of Truncated Icosahedron - (Measured in Meter) - Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Truncated Icosahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = (3*(1+sqrt(5)))/4*le --> (3*(1+sqrt(5)))/4*10
Evaluating ... ...
rm = 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 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
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Indian Institute of Information Technology (IIIT), Bhopal
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5 Midsphere Radius of Truncated Icosahedron Calculators

Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio
Go Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
Midsphere Radius of Truncated Icosahedron given Total Surface Area
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
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
Go Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron
Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron

12 Important Formulas of Truncated Icosahedron Calculators

Volume of Truncated Icosahedron given Total Surface Area
Go Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))))^3
Surface to Volume Ratio of Truncated Icosahedron
Go Surface to Volume Ratio of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Edge Length of Truncated Icosahedron*(125+(43*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Volume
Go Total Surface Area of Truncated Icosahedron = 3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron
Go Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Edge Length of Truncated Icosahedron given Circumsphere Radius
Go Edge Length of Truncated Icosahedron = (4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5))))
Circumsphere Radius of Truncated Icosahedron
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length
Go Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
Edge Length of Truncated Icosahedron given Volume
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
Go Edge Length of Truncated Icosahedron = (4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5)))
Midsphere Radius of Truncated Icosahedron
Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron
Volume of Truncated Icosahedron
Go Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*Edge Length of Truncated Icosahedron^3
Icosahedral Edge Length of Truncated Icosahedron
Go Icosahedral Edge Length of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron

Midsphere Radius of Truncated Icosahedron Formula

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

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?

Midsphere Radius of Truncated Icosahedron calculator uses Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron to calculate the Midsphere Radius of Truncated Icosahedron, Midsphere Radius of Truncated Icosahedron 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. Midsphere Radius of Truncated Icosahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Truncated Icosahedron using this online calculator? To use this online calculator for Midsphere Radius of Truncated Icosahedron, enter Edge Length of Truncated Icosahedron (le) and hit the calculate button. Here is how the Midsphere Radius of Truncated Icosahedron calculation can be explained with given input values -> 24.27051 = (3*(1+sqrt(5)))/4*10.

FAQ

What is Midsphere Radius of Truncated Icosahedron?
Midsphere Radius of Truncated Icosahedron 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 is represented as rm = (3*(1+sqrt(5)))/4*le or Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron. Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.
How to calculate Midsphere Radius of Truncated Icosahedron?
Midsphere Radius of Truncated Icosahedron 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 is calculated using Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron. To calculate Midsphere Radius of Truncated Icosahedron, you need Edge Length of Truncated Icosahedron (le). With our tool, you need to enter the respective value for 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 Edge Length of Truncated Icosahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral 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)
  • Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
  • Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
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