Volume of Truncated Icosahedron given Icosahedral Edge Length Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(Icosahedral Edge Length of Truncated Icosahedron/3)^3
V = (125+(43*sqrt(5)))/4*(le(Icosahedron)/3)^3
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
Volume of Truncated Icosahedron - (Measured in Cubic Meter) - Volume of Truncated Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosahedron.
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
V = (125+(43*sqrt(5)))/4*(le(Icosahedron)/3)^3 --> (125+(43*sqrt(5)))/4*(30/3)^3
Evaluating ... ...
V = 55287.7307581227
STEP 3: Convert Result to Output's Unit
55287.7307581227 Cubic Meter --> No Conversion Required
FINAL ANSWER
55287.7307581227 55287.73 Cubic Meter <-- Volume of Truncated Icosahedron
(Calculation completed in 00.006 seconds)

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Indian Institute of Information Technology (IIIT), Bhopal
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Volume of Truncated Icosahedron Calculators

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

Volume of Truncated Icosahedron given Icosahedral Edge Length Formula

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

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 Volume of Truncated Icosahedron given Icosahedral Edge Length?

Volume of Truncated Icosahedron given Icosahedral Edge Length calculator uses Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(Icosahedral Edge Length of Truncated Icosahedron/3)^3 to calculate the Volume of Truncated Icosahedron, Volume of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosahedron, and calculated using the icosahedral edge length of the Truncated Icosahedron. Volume of Truncated Icosahedron is denoted by V symbol.

How to calculate Volume of Truncated Icosahedron given Icosahedral Edge Length using this online calculator? To use this online calculator for Volume of Truncated Icosahedron given Icosahedral Edge Length, enter Icosahedral Edge Length of Truncated Icosahedron (le(Icosahedron)) and hit the calculate button. Here is how the Volume of Truncated Icosahedron given Icosahedral Edge Length calculation can be explained with given input values -> 55287.73 = (125+(43*sqrt(5)))/4*(30/3)^3.

FAQ

What is Volume of Truncated Icosahedron given Icosahedral Edge Length?
Volume of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosahedron, and calculated using the icosahedral edge length of the Truncated Icosahedron and is represented as V = (125+(43*sqrt(5)))/4*(le(Icosahedron)/3)^3 or Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(Icosahedral Edge Length of Truncated Icosahedron/3)^3. 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 Volume of Truncated Icosahedron given Icosahedral Edge Length?
Volume of Truncated Icosahedron given Icosahedral Edge Length formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosahedron, and calculated using the icosahedral edge length of the Truncated Icosahedron is calculated using Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(Icosahedral Edge Length of Truncated Icosahedron/3)^3. To calculate Volume of Truncated Icosahedron given Icosahedral Edge Length, you need Icosahedral Edge Length of Truncated Icosahedron (le(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 Volume of Truncated Icosahedron?
In this formula, Volume 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 -
  • Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*((4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5)))))^3
  • Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*((4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5))))^3
  • Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*((12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))))^3
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