Short Edge of Pentagonal Hexecontahedron given Insphere Radius Calculator

✖Insphere Radius of Pentagonal Hexecontahedron is the radius of the sphere that is contained by the Pentagonal Hexecontahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Pentagonal Hexecontahedron [r_i]

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✖Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron.ⓘ Short Edge of Pentagonal Hexecontahedron given Insphere Radius [l_e(Short)]

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Short Edge of Pentagonal Hexecontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Pentagonal Hexecontahedron = (Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))
l_e(Short) = (r_i*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))
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

Short Edge of Pentagonal Hexecontahedron - (Measured in Meter) - Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron.
Insphere Radius of Pentagonal Hexecontahedron - (Measured in Meter) - Insphere Radius of Pentagonal Hexecontahedron is the radius of the sphere that is contained by the Pentagonal Hexecontahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentagonal Hexecontahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Short) = (r_i*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))) --> (14*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))

Evaluating ... ...

l_e(Short) = 4.00054191099072

STEP 3: Convert Result to Output's Unit

4.00054191099072 Meter --> No Conversion Required

FINAL ANSWER

4.00054191099072 ≈ 4.000542 Meter <-- Short Edge of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Short Edge of Pentagonal Hexecontahedron Calculators

Short Edge of Pentagonal Hexecontahedron given Long Edge

LaTeX Go Short Edge of Pentagonal Hexecontahedron = (31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756)))

Short Edge of Pentagonal Hexecontahedron given Total Surface Area

LaTeX Go Short Edge of Pentagonal Hexecontahedron = sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))

Short Edge of Pentagonal Hexecontahedron given Volume

LaTeX Go Short Edge of Pentagonal Hexecontahedron = ((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)))^(1/3)

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

LaTeX Go Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))

Short Edge of Pentagonal Hexecontahedron given Insphere Radius Formula

LaTeX Go

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Short Edge of Pentagonal Hexecontahedron given Insphere Radius?

Short Edge of Pentagonal Hexecontahedron given Insphere Radius calculator uses Short Edge of Pentagonal Hexecontahedron = (Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))) to calculate the Short Edge of Pentagonal Hexecontahedron, Short Edge of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using insphere radius of Pentagonal Hexecontahedron. Short Edge of Pentagonal Hexecontahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Pentagonal Hexecontahedron given Insphere Radius using this online calculator? To use this online calculator for Short Edge of Pentagonal Hexecontahedron given Insphere Radius, enter Insphere Radius of Pentagonal Hexecontahedron (r_i) and hit the calculate button. Here is how the Short Edge of Pentagonal Hexecontahedron given Insphere Radius calculation can be explained with given input values -> 4.000542 = (14*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))).

FAQ

What is Short Edge of Pentagonal Hexecontahedron given Insphere Radius?

Short Edge of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using insphere radius of Pentagonal Hexecontahedron and is represented as l_e(Short) = (r_i*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))) or Short Edge of Pentagonal Hexecontahedron = (Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))). Insphere Radius of Pentagonal Hexecontahedron is the radius of the sphere that is contained by the Pentagonal Hexecontahedron in such a way that all the faces just touch the sphere.

How to calculate Short Edge of Pentagonal Hexecontahedron given Insphere Radius?

Short Edge of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using insphere radius of Pentagonal Hexecontahedron is calculated using Short Edge of Pentagonal Hexecontahedron = (Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))). To calculate Short Edge of Pentagonal Hexecontahedron given Insphere Radius, you need Insphere Radius of Pentagonal Hexecontahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Pentagonal Hexecontahedron 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 Short Edge of Pentagonal Hexecontahedron?

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

Short Edge of Pentagonal Hexecontahedron = (31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756)))
Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))
Short Edge of Pentagonal Hexecontahedron = sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))

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