Long Edge of Pentagonal Hexecontahedron given Midsphere Radius Calculator

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

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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 Midsphere Radius [l_e(Long)]

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Long Edge of Pentagonal Hexecontahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
l_e(Long) = (r_m/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
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.
Midsphere Radius of Pentagonal Hexecontahedron - (Measured in Meter) - Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Pentagonal Hexecontahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Long) = (r_m/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 --> (15/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

Evaluating ... ...

l_e(Long) = 5.70113583955334

STEP 3: Convert Result to Output's Unit

5.70113583955334 Meter --> No Conversion Required

FINAL ANSWER

5.70113583955334 ≈ 5.701136 Meter <-- Long Edge of Pentagonal Hexecontahedron

(Calculation completed in 00.020 seconds)

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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 given Midsphere 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 Long Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Long Edge of Pentagonal Hexecontahedron given Midsphere Radius calculator uses 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 to calculate the Long Edge of Pentagonal Hexecontahedron, Long Edge of Pentagonal Hexecontahedron given Midsphere Radius 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 midsphere radius of Pentagonal Hexecontahedron. Long Edge of Pentagonal Hexecontahedron is denoted by l_e(Long) symbol.

How to calculate Long Edge of Pentagonal Hexecontahedron given Midsphere Radius using this online calculator? To use this online calculator for Long Edge of Pentagonal Hexecontahedron given Midsphere Radius, enter Midsphere Radius of Pentagonal Hexecontahedron (r_m) and hit the calculate button. Here is how the Long Edge of Pentagonal Hexecontahedron given Midsphere Radius calculation can be explained with given input values -> 5.701136 = (15/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.

FAQ

What is Long Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Long Edge of Pentagonal Hexecontahedron given Midsphere Radius 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 midsphere radius of Pentagonal Hexecontahedron and is represented as l_e(Long) = (r_m/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 or 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. Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.

How to calculate Long Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Long Edge of Pentagonal Hexecontahedron given Midsphere Radius 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 midsphere radius of Pentagonal Hexecontahedron is calculated using 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. To calculate Long Edge of Pentagonal Hexecontahedron given Midsphere Radius, you need Midsphere Radius of Pentagonal Hexecontahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Long Edge of Pentagonal Hexecontahedron?

In this formula, Long Edge of Pentagonal Hexecontahedron uses Midsphere Radius of Pentagonal Hexecontahedron. We can use 3 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 = (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

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