Midsphere Radius of Truncated Icosidodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron
rm = sqrt(30+(12*sqrt(5)))/2*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 Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Icosidodecahedron is the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere.
Edge Length of Truncated Icosidodecahedron - (Measured in Meter) - Edge Length of Truncated Icosidodecahedron is the length of any edge of the Truncated Icosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Truncated Icosidodecahedron: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(30+(12*sqrt(5)))/2*le --> sqrt(30+(12*sqrt(5)))/2*8
Evaluating ... ...
rm = 30.1550170233737
STEP 3: Convert Result to Output's Unit
30.1550170233737 Meter --> No Conversion Required
FINAL ANSWER
30.1550170233737 30.15502 Meter <-- Midsphere Radius of Truncated Icosidodecahedron
(Calculation completed in 00.020 seconds)

Credits

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5 Midsphere Radius of Truncated Icosidodecahedron Calculators

Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area
Go Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
Midsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio
Go Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
Midsphere Radius of Truncated Icosidodecahedron given Circumsphere Radius
Go Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))*Circumsphere Radius of Truncated Icosidodecahedron/sqrt(31+(12*sqrt(5)))
Midsphere Radius of Truncated Icosidodecahedron given Volume
Go Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
Midsphere Radius of Truncated Icosidodecahedron
Go Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron

Midsphere Radius of Truncated Icosidodecahedron Formula

Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron
rm = sqrt(30+(12*sqrt(5)))/2*le

What is a Truncated Icosidodecahedron?

In geometry, the Truncated Icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. It has 62 faces which include 30 squares, 20 regular hexagons and 12 regular decagons. Each vertex is identical in such a way that, one square, one hexagon and one decagon join at each vertex. It has the most edges and vertices of all Platonic and Archimedean solids, though the snub dodecahedron has more number of faces. Out of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the Snub Dodecahedron (89.63%) and Small Rhombicosidodecahedron (89.23%), and less narrowly beating the Truncated Icosahedron (86.74%).

How to Calculate Midsphere Radius of Truncated Icosidodecahedron?

Midsphere Radius of Truncated Icosidodecahedron calculator uses Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron to calculate the Midsphere Radius of Truncated Icosidodecahedron, Midsphere Radius of Truncated Icosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere. Midsphere Radius of Truncated Icosidodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Truncated Icosidodecahedron using this online calculator? To use this online calculator for Midsphere Radius of Truncated Icosidodecahedron, enter Edge Length of Truncated Icosidodecahedron (le) and hit the calculate button. Here is how the Midsphere Radius of Truncated Icosidodecahedron calculation can be explained with given input values -> 30.15502 = sqrt(30+(12*sqrt(5)))/2*8.

FAQ

What is Midsphere Radius of Truncated Icosidodecahedron?
Midsphere Radius of Truncated Icosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere and is represented as rm = sqrt(30+(12*sqrt(5)))/2*le or Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron. Edge Length of Truncated Icosidodecahedron is the length of any edge of the Truncated Icosidodecahedron.
How to calculate Midsphere Radius of Truncated Icosidodecahedron?
Midsphere Radius of Truncated Icosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere is calculated using Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron. To calculate Midsphere Radius of Truncated Icosidodecahedron, you need Edge Length of Truncated Icosidodecahedron (le). With our tool, you need to enter the respective value for Edge Length of Truncated Icosidodecahedron 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 Icosidodecahedron?
In this formula, Midsphere Radius of Truncated Icosidodecahedron uses Edge Length of Truncated Icosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))*Circumsphere Radius of Truncated Icosidodecahedron/sqrt(31+(12*sqrt(5)))
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
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