Long Edge of Pentagonal Hexecontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
le(Long) = ((ri*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
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.
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
le(Long) = ((ri*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 --> ((14*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
Evaluating ... ...
le(Long) = 5.47021750418332
STEP 3: Convert Result to Output's Unit
5.47021750418332 Meter --> No Conversion Required
FINAL ANSWER
5.47021750418332 5.470218 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 Insphere Radius Formula

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
le(Long) = ((ri*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

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 Insphere Radius?

Long Edge of Pentagonal Hexecontahedron given Insphere Radius calculator uses 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 to calculate the Long Edge of Pentagonal Hexecontahedron, Long Edge of Pentagonal Hexecontahedron given Insphere 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 insphere radius of Pentagonal Hexecontahedron. Long Edge of Pentagonal Hexecontahedron is denoted by le(Long) symbol.

How to calculate Long Edge of Pentagonal Hexecontahedron given Insphere Radius using this online calculator? To use this online calculator for Long Edge of Pentagonal Hexecontahedron given Insphere Radius, enter Insphere Radius of Pentagonal Hexecontahedron (ri) and hit the calculate button. Here is how the Long Edge of Pentagonal Hexecontahedron given Insphere Radius calculation can be explained with given input values -> 5.470218 = ((14*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.

FAQ

What is Long Edge of Pentagonal Hexecontahedron given Insphere Radius?
Long Edge of Pentagonal Hexecontahedron given Insphere 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 insphere radius of Pentagonal Hexecontahedron and is represented as le(Long) = ((ri*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 or 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. 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 Long Edge of Pentagonal Hexecontahedron given Insphere Radius?
Long Edge of Pentagonal Hexecontahedron given Insphere 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 insphere radius of Pentagonal Hexecontahedron is calculated using 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. To calculate Long Edge of Pentagonal Hexecontahedron given Insphere Radius, you need Insphere Radius of Pentagonal Hexecontahedron (ri). 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 Long Edge of Pentagonal Hexecontahedron?
In this formula, Long Edge of Pentagonal Hexecontahedron uses Insphere Radius of 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 = (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
  • 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 = ((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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