Edge Length of Great Dodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.ⓘ Circumsphere Radius of Great Dodecahedron [r_c]

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✖Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.ⓘ Edge Length of Great Dodecahedron given Circumsphere Radius [l_e]

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Edge Length of Great Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))
l_e = (4*r_c)/sqrt(10+(2*sqrt(5)))
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

Edge Length of Great Dodecahedron - (Measured in Meter) - Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.
Circumsphere Radius of Great Dodecahedron - (Measured in Meter) - Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Great Dodecahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (4*r_c)/sqrt(10+(2*sqrt(5))) --> (4*9)/sqrt(10+(2*sqrt(5)))

Evaluating ... ...

l_e = 9.46316001814441

STEP 3: Convert Result to Output's Unit

9.46316001814441 Meter --> No Conversion Required

FINAL ANSWER

9.46316001814441 ≈ 9.46316 Meter <-- Edge Length of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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< Edge Length of Great Dodecahedron Calculators

Edge Length of Great Dodecahedron given Total Surface Area

LaTeX Go Edge Length of Great Dodecahedron = sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Edge Length of Great Dodecahedron given Circumsphere Radius

LaTeX Go Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))

Edge Length of Great Dodecahedron given Pyramidal Height

LaTeX Go Edge Length of Great Dodecahedron = (6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))

Edge Length of Great Dodecahedron given Ridge Length

LaTeX Go Edge Length of Great Dodecahedron = (2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Edge Length of Great Dodecahedron given Circumsphere Radius Formula

LaTeX Go

Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))
l_e = (4*r_c)/sqrt(10+(2*sqrt(5)))

What is Great Dodecahedron ?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Edge Length of Great Dodecahedron given Circumsphere Radius?

Edge Length of Great Dodecahedron given Circumsphere Radius calculator uses Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))) to calculate the Edge Length of Great Dodecahedron, Edge Length of Great Dodecahedron given Circumsphere Radius formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its circumsphere radius. Edge Length of Great Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Great Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Edge Length of Great Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Great Dodecahedron (r_c) and hit the calculate button. Here is how the Edge Length of Great Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 9.46316 = (4*9)/sqrt(10+(2*sqrt(5))).

FAQ

What is Edge Length of Great Dodecahedron given Circumsphere Radius?

Edge Length of Great Dodecahedron given Circumsphere Radius formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its circumsphere radius and is represented as l_e = (4*r_c)/sqrt(10+(2*sqrt(5))) or Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))). Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.

How to calculate Edge Length of Great Dodecahedron given Circumsphere Radius?

Edge Length of Great Dodecahedron given Circumsphere Radius formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its circumsphere radius is calculated using Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))). To calculate Edge Length of Great Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Great Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Great Dodecahedron 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 Edge Length of Great Dodecahedron?

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

Edge Length of Great Dodecahedron = (2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Edge Length of Great Dodecahedron = (6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
Edge Length of Great Dodecahedron = sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

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