Snub Dodecahedron 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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✖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 of Pentagonal Hexecontahedron given Midsphere Radius [l_{e(Snub Dodecahedron)}]

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Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Snub Dodecahedron Edge Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756))
l_{e(Snub Dodecahedron)} = r_m/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*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

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.
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(Snub Dodecahedron)} = r_m/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)) --> 15/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756))

Evaluating ... ...

l_{e(Snub Dodecahedron)} = 7.15289591703948

STEP 3: Convert Result to Output's Unit

7.15289591703948 Meter --> No Conversion Required

FINAL ANSWER

7.15289591703948 ≈ 7.152896 Meter <-- Snub Dodecahedron Edge Pentagonal Hexecontahedron

(Calculation completed in 00.018 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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< Snub Dodecahedron Edge of Pentagonal Hexecontahedron Calculators

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Long Edge

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

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Total Surface Area

LaTeX Go Snub Dodecahedron Edge 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))

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Volume

LaTeX Go Snub Dodecahedron Edge 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))

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius

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

Snub Dodecahedron 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 Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius calculator uses Snub Dodecahedron Edge Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)) to calculate the Snub Dodecahedron Edge Pentagonal Hexecontahedron, Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron. Snub Dodecahedron Edge Pentagonal Hexecontahedron is denoted by l_{e(Snub Dodecahedron)} symbol.

How to calculate Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius using this online calculator? To use this online calculator for Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius, enter Midsphere Radius of Pentagonal Hexecontahedron (r_m) and hit the calculate button. Here is how the Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius calculation can be explained with given input values -> 7.152896 = 15/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)).

FAQ

What is Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron and is represented as l_{e(Snub Dodecahedron)} = r_m/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)) or Snub Dodecahedron Edge Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)). 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 Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Snub Dodecahedron Edge of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron of which the dual body is the Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron is calculated using Snub Dodecahedron Edge Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756)))*sqrt(2+2*(0.4715756)). To calculate Snub Dodecahedron 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 Snub Dodecahedron Edge Pentagonal Hexecontahedron?

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

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

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