Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Calculator

✖Snub Dodecahedron Edge Pentagonal Hexecontahedron is the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron.ⓘ Snub Dodecahedron Edge Pentagonal Hexecontahedron [l_{e(Snub Dodecahedron)}]

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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 Snub Dodecahedron Edge [l_e(Short)]

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Formula

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Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

Formula

`"l"_{"e(Short)"} = "l"_{"e(Snub Dodecahedron)"}/sqrt(2+2*(0.4715756))`

Example

`"4.080297m"="7m"/sqrt(2+2*(0.4715756))`

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Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))
l_e(Short) = l_{e(Snub Dodecahedron)}/sqrt(2+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.
Snub Dodecahedron Edge Pentagonal Hexecontahedron - (Measured in Meter) - Snub Dodecahedron Edge Pentagonal Hexecontahedron is the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron.

STEP 1: Convert Input(s) to Base Unit

Snub Dodecahedron Edge Pentagonal Hexecontahedron: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Short) = l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756)) --> 7/sqrt(2+2*(0.4715756))

Evaluating ... ...

l_e(Short) = 4.08029678428185

STEP 3: Convert Result to Output's Unit

4.08029678428185 Meter --> No Conversion Required

FINAL ANSWER

4.08029678428185 ≈ 4.080297 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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< 7 Short Edge of Pentagonal Hexecontahedron Calculators

Short Edge of Pentagonal Hexecontahedron given Long Edge

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 Surface to Volume Ratio

Go Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))

Short Edge of Pentagonal Hexecontahedron given Total Surface Area

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

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 Insphere Radius

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

Short Edge of Pentagonal Hexecontahedron given Midsphere Radius

Go Short Edge of Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

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

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula

Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))
l_e(Short) = l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756))

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 Snub Dodecahedron Edge?

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge calculator uses Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)) to calculate the Short Edge of Pentagonal Hexecontahedron, Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge 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 snub dodecahedron edge of Pentagonal Hexecontahedron. Short Edge of Pentagonal Hexecontahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge using this online calculator? To use this online calculator for Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge, enter Snub Dodecahedron Edge Pentagonal Hexecontahedron (l_{e(Snub Dodecahedron)}) and hit the calculate button. Here is how the Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge calculation can be explained with given input values -> 4.080297 = 7/sqrt(2+2*(0.4715756)).

FAQ

What is Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge?

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge 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 snub dodecahedron edge of Pentagonal Hexecontahedron and is represented as l_e(Short) = l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756)) or Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)). Snub Dodecahedron Edge Pentagonal Hexecontahedron is the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron.

How to calculate Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge?

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge 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 snub dodecahedron edge of Pentagonal Hexecontahedron is calculated using Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)). To calculate Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge, you need Snub Dodecahedron Edge Pentagonal Hexecontahedron (l_{e(Snub Dodecahedron)}). With our tool, you need to enter the respective value for Snub Dodecahedron Edge 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 Snub Dodecahedron Edge Pentagonal Hexecontahedron. We can use 6 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 = 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 = ((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 = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))
Short Edge of Pentagonal Hexecontahedron = (Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))
Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))

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