Insphere Radius of Pentagonal Icositetrahedron given Long Edge Calculator

✖Long Edge of Pentagonal Icositetrahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Icositetrahedron.ⓘ Long Edge of Pentagonal Icositetrahedron [l_e(Long)]

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✖Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.ⓘ Insphere Radius of Pentagonal Icositetrahedron given Long Edge [r_i]

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Insphere Radius of Pentagonal Icositetrahedron given Long Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))
r_i = l_e(Long)/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[Tribonacci_C] - Tribonacci constant Value Taken As 1.839286755214161

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

Insphere Radius of Pentagonal Icositetrahedron - (Measured in Meter) - Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.
Long Edge of Pentagonal Icositetrahedron - (Measured in Meter) - Long Edge of Pentagonal Icositetrahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Icositetrahedron.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Pentagonal Icositetrahedron: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = l_e(Long)/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)) --> 8/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))

Evaluating ... ...

r_i = 10.9925146698337

STEP 3: Convert Result to Output's Unit

10.9925146698337 Meter --> No Conversion Required

FINAL ANSWER

10.9925146698337 ≈ 10.99251 Meter <-- Insphere Radius of Pentagonal Icositetrahedron

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Insphere Radius of Pentagonal Icositetrahedron Calculators

Insphere Radius of Pentagonal Icositetrahedron given Surface to Volume Ratio

LaTeX Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))

Insphere Radius of Pentagonal Icositetrahedron given Total Surface Area

LaTeX Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(sqrt(Total Surface Area of Pentagonal Icositetrahedron/3)*(((4*[Tribonacci_C])-3)/(22*((5*[Tribonacci_C])-1)))^(1/4))

Insphere Radius of Pentagonal Icositetrahedron given Volume

LaTeX Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))

Insphere Radius of Pentagonal Icositetrahedron given Long Edge

LaTeX Go Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))

Insphere Radius of Pentagonal Icositetrahedron given Long Edge Formula

LaTeX Go

What is Pentagonal Icositetrahedron?

The Pentagonal Icositetrahedron can be constructed from a snub cube. Its faces are axial-symmetric pentagons with the top angle acos(2-t)=80.7517°. Of this polyhedron, there are two forms that are mirror images of each other, but otherwise identical. It has 24 faces, 60 edges, and 38 vertices.

How to Calculate Insphere Radius of Pentagonal Icositetrahedron given Long Edge?

Insphere Radius of Pentagonal Icositetrahedron given Long Edge calculator uses Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)) to calculate the Insphere Radius of Pentagonal Icositetrahedron, Insphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the long edge of Pentagonal Icositetrahedron. Insphere Radius of Pentagonal Icositetrahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Pentagonal Icositetrahedron given Long Edge using this online calculator? To use this online calculator for Insphere Radius of Pentagonal Icositetrahedron given Long Edge, enter Long Edge of Pentagonal Icositetrahedron (l_e(Long)) and hit the calculate button. Here is how the Insphere Radius of Pentagonal Icositetrahedron given Long Edge calculation can be explained with given input values -> 10.99251 = 8/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)).

FAQ

What is Insphere Radius of Pentagonal Icositetrahedron given Long Edge?

Insphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the long edge of Pentagonal Icositetrahedron and is represented as r_i = l_e(Long)/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)) or Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)). Long Edge of Pentagonal Icositetrahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Icositetrahedron.

How to calculate Insphere Radius of Pentagonal Icositetrahedron given Long Edge?

Insphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the long edge of Pentagonal Icositetrahedron is calculated using Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1)). To calculate Insphere Radius of Pentagonal Icositetrahedron given Long Edge, you need Long Edge of Pentagonal Icositetrahedron (l_e(Long)). With our tool, you need to enter the respective value for Long Edge of Pentagonal Icositetrahedron 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 Insphere Radius of Pentagonal Icositetrahedron?

In this formula, Insphere Radius of Pentagonal Icositetrahedron uses Long Edge of Pentagonal Icositetrahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(sqrt(Total Surface Area of Pentagonal Icositetrahedron/3)*(((4*[Tribonacci_C])-3)/(22*((5*[Tribonacci_C])-1)))^(1/4))
Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))

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