Midsphere 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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✖Midsphere Radius of Pentagonal Icositetrahedron is the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Pentagonal Icositetrahedron given Long Edge [r_m]

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Formula

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Midsphere Radius of Pentagonal Icositetrahedron given Long Edge

Formula

`"r"_{"m"} = 1/sqrt(2-"[Tribonacci_C]")*(("l"_{"e(Long)"})/sqrt("[Tribonacci_C]"+1))`

Example

`"11.84294m"=1/sqrt(2-"[Tribonacci_C]")*(("8m")/sqrt("[Tribonacci_C]"+1))`

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Midsphere Radius of Pentagonal Icositetrahedron given Long Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Pentagonal Icositetrahedron = 1/sqrt(2-[Tribonacci_C])*((Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1))
r_m = 1/sqrt(2-[Tribonacci_C])*((l_e(Long))/sqrt([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

Midsphere Radius of Pentagonal Icositetrahedron - (Measured in Meter) - Midsphere Radius of Pentagonal Icositetrahedron is the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that 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_m = 1/sqrt(2-[Tribonacci_C])*((l_e(Long))/sqrt([Tribonacci_C]+1)) --> 1/sqrt(2-[Tribonacci_C])*((8)/sqrt([Tribonacci_C]+1))

Evaluating ... ...

r_m = 11.8429398619177

STEP 3: Convert Result to Output's Unit

11.8429398619177 Meter --> No Conversion Required

FINAL ANSWER

11.8429398619177 ≈ 11.84294 Meter <-- Midsphere Radius of Pentagonal Icositetrahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 7 Midsphere Radius of Pentagonal Icositetrahedron Calculators

Midsphere Radius of Pentagonal Icositetrahedron given Surface to Volume Ratio

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

Midsphere Radius of Pentagonal Icositetrahedron given Total Surface Area

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

Midsphere Radius of Pentagonal Icositetrahedron given Volume

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

Midsphere Radius of Pentagonal Icositetrahedron given Short Edge

Go Midsphere Radius of Pentagonal Icositetrahedron = (sqrt([Tribonacci_C]+1)*Short Edge of Pentagonal Icositetrahedron)/(2*sqrt(2-[Tribonacci_C]))

Midsphere Radius of Pentagonal Icositetrahedron given Long Edge

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

Midsphere Radius of Pentagonal Icositetrahedron

Go Midsphere Radius of Pentagonal Icositetrahedron = Snub Cube Edge of Pentagonal Icositetrahedron/(2*sqrt(2-[Tribonacci_C]))

Midsphere Radius of Pentagonal Icositetrahedron given Insphere Radius

Go Midsphere Radius of Pentagonal Icositetrahedron = sqrt(3-[Tribonacci_C])*Insphere Radius of Pentagonal Icositetrahedron

Midsphere Radius of Pentagonal Icositetrahedron given Long Edge Formula

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 Midsphere Radius of Pentagonal Icositetrahedron given Long Edge?

Midsphere Radius of Pentagonal Icositetrahedron given Long Edge calculator uses Midsphere Radius of Pentagonal Icositetrahedron = 1/sqrt(2-[Tribonacci_C])*((Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1)) to calculate the Midsphere Radius of Pentagonal Icositetrahedron, Midsphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that sphere, calculated using the long edge of Pentagonal Icositetrahedron. Midsphere Radius of Pentagonal Icositetrahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Pentagonal Icositetrahedron given Long Edge using this online calculator? To use this online calculator for Midsphere 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 Midsphere Radius of Pentagonal Icositetrahedron given Long Edge calculation can be explained with given input values -> 11.84294 = 1/sqrt(2-[Tribonacci_C])*((8)/sqrt([Tribonacci_C]+1)).

FAQ

What is Midsphere Radius of Pentagonal Icositetrahedron given Long Edge?

Midsphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that sphere, calculated using the long edge of Pentagonal Icositetrahedron and is represented as r_m = 1/sqrt(2-[Tribonacci_C])*((l_e(Long))/sqrt([Tribonacci_C]+1)) or Midsphere Radius of Pentagonal Icositetrahedron = 1/sqrt(2-[Tribonacci_C])*((Long Edge of Pentagonal Icositetrahedron)/sqrt([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 Midsphere Radius of Pentagonal Icositetrahedron given Long Edge?

Midsphere Radius of Pentagonal Icositetrahedron given Long Edge formula is defined as the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that sphere, calculated using the long edge of Pentagonal Icositetrahedron is calculated using Midsphere Radius of Pentagonal Icositetrahedron = 1/sqrt(2-[Tribonacci_C])*((Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1)). To calculate Midsphere 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 Midsphere Radius of Pentagonal Icositetrahedron?

In this formula, Midsphere Radius of Pentagonal Icositetrahedron uses Long Edge of Pentagonal Icositetrahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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