Edge Length of Great Stellated Dodecahedron given Circumradius Calculator

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

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

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Edge Length of Great Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
l_e = (4*r_c)/(sqrt(3)*(3+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 Stellated Dodecahedron - (Measured in Meter) - Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron.
Circumradius of Great Stellated Dodecahedron - (Measured in Meter) - Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Great Stellated Dodecahedron: 23 Meter --> 23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (4*r_c)/(sqrt(3)*(3+sqrt(5))) --> (4*23)/(sqrt(3)*(3+sqrt(5)))

Evaluating ... ...

l_e = 10.1442962531606

STEP 3: Convert Result to Output's Unit

10.1442962531606 Meter --> No Conversion Required

FINAL ANSWER

10.1442962531606 ≈ 10.1443 Meter <-- Edge Length of Great Stellated Dodecahedron

(Calculation completed in 00.006 seconds)

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< Edge Length of Great Stellated Dodecahedron Calculators

Edge Length of Great Stellated Dodecahedron given Pyramidal Height

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

Edge Length of Great Stellated Dodecahedron given Circumradius

LaTeX Go Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

Edge Length of Great Stellated Dodecahedron given Ridge Length

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

Edge Length of Great Stellated Dodecahedron given Pentagram Chord

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

Edge Length of Great Stellated Dodecahedron given Circumradius Formula

LaTeX Go

Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
l_e = (4*r_c)/(sqrt(3)*(3+sqrt(5)))

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

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

Edge Length of Great Stellated Dodecahedron given Circumradius calculator uses Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Edge Length of Great Stellated Dodecahedron, Edge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron, calculated using its circumradius. Edge Length of Great Stellated Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Great Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Edge Length of Great Stellated Dodecahedron given Circumradius, enter Circumradius of Great Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Edge Length of Great Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 10.1443 = (4*23)/(sqrt(3)*(3+sqrt(5))).

FAQ

What is Edge Length of Great Stellated Dodecahedron given Circumradius?

Edge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron, calculated using its circumradius and is represented as l_e = (4*r_c)/(sqrt(3)*(3+sqrt(5))) or Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))). Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

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

Edge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron, calculated using its circumradius is calculated using Edge Length of Great Stellated Dodecahedron = (4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Edge Length of Great Stellated Dodecahedron given Circumradius, you need Circumradius of Great Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius of Great 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 Great Stellated Dodecahedron?

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

Edge Length of Great Stellated Dodecahedron = (2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Edge Length of Great Stellated Dodecahedron = Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
Edge Length of Great Stellated Dodecahedron = (6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

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