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

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Formula

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Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

Formula

`"l"_{"e(Long)"} = ("l"_{"e(Snub Dodecahedron)"}/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*"[phi]"+2)+(5*"[phi]"-3)+2*(8-3*"[phi]")))/31`

Example

`"5.579272m"=("7m"/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*"[phi]"+2)+(5*"[phi]"-3)+2*(8-3*"[phi]")))/31`

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Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Edge of Pentagonal Hexecontahedron = (Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
l_e(Long) = (l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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

Long Edge of Pentagonal Hexecontahedron - (Measured in Meter) - Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of 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(Long) = (l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 --> (7/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Evaluating ... ...

l_e(Long) = 5.57927185572566

STEP 3: Convert Result to Output's Unit

5.57927185572566 Meter --> No Conversion Required

FINAL ANSWER

5.57927185572566 ≈ 5.579272 Meter <-- Long Edge of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< 7 Long Edge of Pentagonal Hexecontahedron Calculators

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio

Go Long 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)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Long Edge of Pentagonal Hexecontahedron given Total Surface Area

Go Long 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)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Long Edge of Pentagonal Hexecontahedron given Volume

Go Long 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)*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Long Edge of Pentagonal Hexecontahedron given Insphere Radius

Go Long Edge of Pentagonal Hexecontahedron = ((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Long Edge of Pentagonal Hexecontahedron given Midsphere Radius

Go Long Edge of Pentagonal Hexecontahedron = (Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

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

Long Edge of Pentagonal Hexecontahedron

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

Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula

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 Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge?

Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge calculator uses Long Edge of Pentagonal Hexecontahedron = (Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 to calculate the Long Edge of Pentagonal Hexecontahedron, Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron, calculated using snub dodecahedron edge of Pentagonal Hexecontahedron. Long Edge of Pentagonal Hexecontahedron is denoted by l_e(Long) symbol.

How to calculate Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge using this online calculator? To use this online calculator for Long 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 Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge calculation can be explained with given input values -> 5.579272 = (7/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31.

FAQ

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

Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron, calculated using snub dodecahedron edge of Pentagonal Hexecontahedron and is represented as l_e(Long) = (l_{e(Snub Dodecahedron)}/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 or Long Edge of Pentagonal Hexecontahedron = (Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31. 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 Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge?

Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron, calculated using snub dodecahedron edge of Pentagonal Hexecontahedron is calculated using Long Edge of Pentagonal Hexecontahedron = (Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31. To calculate Long 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 Long Edge of Pentagonal Hexecontahedron?

In this formula, Long 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 -

Long Edge of Pentagonal Hexecontahedron = (Short Edge of Pentagonal Hexecontahedron*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long 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)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long 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)*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long Edge of Pentagonal Hexecontahedron = (Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long Edge of Pentagonal Hexecontahedron = ((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756))))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long 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)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

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