Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height Calculator

✖Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Height of Icosidodecahedron [h_Pentagon]

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✖Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height [r_c]

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Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5)))
r_c = (1+sqrt(5))*h_Pentagon/sqrt(5+(2*sqrt(5)))
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

Circumsphere Radius of Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.
Pentagonal Face Height of Icosidodecahedron - (Measured in Meter) - Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagonal Face Height of Icosidodecahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (1+sqrt(5))*h_Pentagon/sqrt(5+(2*sqrt(5))) --> (1+sqrt(5))*15/sqrt(5+(2*sqrt(5)))

Evaluating ... ...

r_c = 15.771933363574

STEP 3: Convert Result to Output's Unit

15.771933363574 Meter --> No Conversion Required

FINAL ANSWER

15.771933363574 ≈ 15.77193 Meter <-- Circumsphere Radius of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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The National Institute of Engineering (NIE), Mysuru

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< Circumsphere Radius of Icosidodecahedron Calculators

Circumsphere Radius of Icosidodecahedron given Total Surface Area

LaTeX Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Circumsphere Radius of Icosidodecahedron given Midsphere Radius

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

Circumsphere Radius of Icosidodecahedron given Volume

LaTeX Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

Circumsphere Radius of Icosidodecahedron

LaTeX Go Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*Edge Length of Icosidodecahedron

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height Formula

LaTeX Go

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5)))
r_c = (1+sqrt(5))*h_Pentagon/sqrt(5+(2*sqrt(5)))

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height?

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height calculator uses Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5))) to calculate the Circumsphere Radius of Icosidodecahedron, Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the pentagonal face height of the Icosidodecahedron. Circumsphere Radius of Icosidodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height using this online calculator? To use this online calculator for Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height, enter Pentagonal Face Height of Icosidodecahedron (h_Pentagon) and hit the calculate button. Here is how the Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height calculation can be explained with given input values -> 15.77193 = (1+sqrt(5))*15/sqrt(5+(2*sqrt(5))).

FAQ

What is Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height?

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the pentagonal face height of the Icosidodecahedron and is represented as r_c = (1+sqrt(5))*h_Pentagon/sqrt(5+(2*sqrt(5))) or Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5))). Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

How to calculate Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height?

Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height formula is defined as the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the pentagonal face height of the Icosidodecahedron is calculated using Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))*Pentagonal Face Height of Icosidodecahedron/sqrt(5+(2*sqrt(5))). To calculate Circumsphere Radius of Icosidodecahedron given Pentagonal Face Height, you need Pentagonal Face Height of Icosidodecahedron (h_Pentagon). With our tool, you need to enter the respective value for Pentagonal Face Height of 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 Circumsphere Radius of Icosidodecahedron?

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

Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*Edge Length of Icosidodecahedron
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Circumsphere Radius of Icosidodecahedron = (1+sqrt(5))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

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