Edge Length of Small Stellated Dodecahedron given Circumradius Calculator

✖Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.ⓘ Circumradius of Small Stellated Dodecahedron [r_c]

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✖Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.ⓘ Edge Length of Small Stellated Dodecahedron given Circumradius [l_e]

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Formula

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Edge Length of Small Stellated Dodecahedron given Circumradius

Formula

`"l"_{"e"} = (4*"r"_{"c"})/(sqrt(50+22*sqrt(5)))`

Example

`"10.04057m"=(4*"25m")/(sqrt(50+22*sqrt(5)))`

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Edge Length of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))
l_e = (4*r_c)/(sqrt(50+22*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 Small Stellated Dodecahedron - (Measured in Meter) - Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.
Circumradius of Small Stellated Dodecahedron - (Measured in Meter) - Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Small Stellated Dodecahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (4*r_c)/(sqrt(50+22*sqrt(5))) --> (4*25)/(sqrt(50+22*sqrt(5)))

Evaluating ... ...

l_e = 10.0405707943114

STEP 3: Convert Result to Output's Unit

10.0405707943114 Meter --> No Conversion Required

FINAL ANSWER

10.0405707943114 ≈ 10.04057 Meter <-- Edge Length of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< 7 Edge Length of Small Stellated Dodecahedron Calculators

Edge Length of Small Stellated Dodecahedron given Surface to Volume Ratio

Go Edge Length of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron)

Edge Length of Small Stellated Dodecahedron given Total Surface Area

Go Edge Length of Small Stellated Dodecahedron = sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))

Edge Length of Small Stellated Dodecahedron given Pyramidal Height

Go Edge Length of Small Stellated Dodecahedron = (5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5)))

Edge Length of Small Stellated Dodecahedron given Circumradius

Go Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))

Edge Length of Small Stellated Dodecahedron given Volume

Go Edge Length of Small Stellated Dodecahedron = ((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3)

Edge Length of Small Stellated Dodecahedron given Ridge Length

Go Edge Length of Small Stellated Dodecahedron = (2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5))

Edge Length of Small Stellated Dodecahedron given Pentagram Chord

Go Edge Length of Small Stellated Dodecahedron = Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5))

Edge Length of Small Stellated Dodecahedron given Circumradius Formula

Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))
l_e = (4*r_c)/(sqrt(50+22*sqrt(5)))

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

How to Calculate Edge Length of Small Stellated Dodecahedron given Circumradius?

Edge Length of Small Stellated Dodecahedron given Circumradius calculator uses Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))) to calculate the Edge Length of Small Stellated Dodecahedron, Edge Length of Small Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron, calculated using its circumradius. Edge Length of Small Stellated Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Edge Length of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Edge Length of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 10.04057 = (4*25)/(sqrt(50+22*sqrt(5))).

FAQ

What is Edge Length of Small Stellated Dodecahedron given Circumradius?

Edge Length of Small Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron, calculated using its circumradius and is represented as l_e = (4*r_c)/(sqrt(50+22*sqrt(5))) or Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))). Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.

How to calculate Edge Length of Small Stellated Dodecahedron given Circumradius?

Edge Length of Small Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron, calculated using its circumradius is calculated using Edge Length of Small Stellated Dodecahedron = (4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))). To calculate Edge Length of Small Stellated Dodecahedron given Circumradius, you need Circumradius of Small Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius of Small Stellated 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 Small Stellated Dodecahedron?

In this formula, Edge Length of Small Stellated Dodecahedron uses Circumradius of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Edge Length of Small Stellated Dodecahedron = (2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5))
Edge Length of Small Stellated Dodecahedron = Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5))
Edge Length of Small Stellated Dodecahedron = (5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5)))
Edge Length of Small Stellated Dodecahedron = sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))
Edge Length of Small Stellated Dodecahedron = ((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3)
Edge Length of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron)

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