Long Edge of Pentagonal Hexecontahedron Calculator

✖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 [l_e(Short)]

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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 [l_e(Long)]

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Long Edge of Pentagonal Hexecontahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
l_e(Long) = (l_e(Short)*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.
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.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Pentagonal Hexecontahedron: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Long) = (l_e(Short)*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 --> (4*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Evaluating ... ...

l_e(Long) = 5.46947651182451

STEP 3: Convert Result to Output's Unit

5.46947651182451 Meter --> No Conversion Required

FINAL ANSWER

5.46947651182451 ≈ 5.469477 Meter <-- Long 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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Indian Institute of Information Technology (IIIT), Bhopal

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< Long Edge of Pentagonal Hexecontahedron Calculators

Long Edge of Pentagonal Hexecontahedron given Total Surface Area

LaTeX 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

LaTeX 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 Snub Dodecahedron Edge

LaTeX 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

LaTeX 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 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 Long Edge of Pentagonal Hexecontahedron?

Long Edge of Pentagonal Hexecontahedron calculator uses 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 to calculate the Long Edge of Pentagonal Hexecontahedron, Long Edge of Pentagonal Hexecontahedron formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron. Long Edge of Pentagonal Hexecontahedron is denoted by l_e(Long) symbol.

How to calculate Long Edge of Pentagonal Hexecontahedron using this online calculator? To use this online calculator for Long Edge of Pentagonal Hexecontahedron, enter Short Edge of Pentagonal Hexecontahedron (l_e(Short)) and hit the calculate button. Here is how the Long Edge of Pentagonal Hexecontahedron calculation can be explained with given input values -> 5.469477 = (4*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31.

FAQ

What is Long Edge of Pentagonal Hexecontahedron?

Long Edge of Pentagonal Hexecontahedron formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron and is represented as l_e(Long) = (l_e(Short)*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 or 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. 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.

How to calculate Long Edge of Pentagonal Hexecontahedron?

Long Edge of Pentagonal Hexecontahedron formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron is calculated using 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. To calculate Long Edge of Pentagonal Hexecontahedron, you need Short Edge of Pentagonal Hexecontahedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge 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 Long Edge of Pentagonal Hexecontahedron?

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

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 = (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

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