Ridge Length of Great Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
lRidge = (1+sqrt(5))/2*(4*rc)/(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
Ridge Length of Great Stellated Dodecahedron - (Measured in Meter) - Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex 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
lRidge = (1+sqrt(5))/2*(4*rc)/(sqrt(3)*(3+sqrt(5))) --> (1+sqrt(5))/2*(4*23)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
lRidge = 16.4138161295621
STEP 3: Convert Result to Output's Unit
16.4138161295621 Meter --> No Conversion Required
FINAL ANSWER
16.4138161295621 16.41382 Meter <-- Ridge Length of Great Stellated Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

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Walchand College of Engineering (WCE), Sangli
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7 Ridge Length of Great Stellated Dodecahedron Calculators

Ridge Length of Great Stellated Dodecahedron given Total Surface Area
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
Ridge Length of Great Stellated Dodecahedron given Surface to Volume Ratio
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)
Ridge Length of Great Stellated Dodecahedron given Pyramidal Height
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Ridge Length of Great Stellated Dodecahedron given Circumradius
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Ridge Length of Great Stellated Dodecahedron given Volume
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
Ridge Length of Great Stellated Dodecahedron given Pentagram Chord
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
Ridge Length of Great Stellated Dodecahedron
Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*Edge Length of Great Stellated Dodecahedron

Ridge Length of Great Stellated Dodecahedron given Circumradius Formula

Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
lRidge = (1+sqrt(5))/2*(4*rc)/(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 Ridge Length of Great Stellated Dodecahedron given Circumradius?

Ridge Length of Great Stellated Dodecahedron given Circumradius calculator uses Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Ridge Length of Great Stellated Dodecahedron, Ridge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its circumradius. Ridge Length of Great Stellated Dodecahedron is denoted by lRidge symbol.

How to calculate Ridge Length of Great Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Ridge Length of Great Stellated Dodecahedron given Circumradius, enter Circumradius of Great Stellated Dodecahedron (rc) and hit the calculate button. Here is how the Ridge Length of Great Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 16.41382 = (1+sqrt(5))/2*(4*23)/(sqrt(3)*(3+sqrt(5))).

FAQ

What is Ridge Length of Great Stellated Dodecahedron given Circumradius?
Ridge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its circumradius and is represented as lRidge = (1+sqrt(5))/2*(4*rc)/(sqrt(3)*(3+sqrt(5))) or Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(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 Ridge Length of Great Stellated Dodecahedron given Circumradius?
Ridge Length of Great Stellated Dodecahedron given Circumradius formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its circumradius is calculated using Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Ridge Length of Great Stellated Dodecahedron given Circumradius, you need Circumradius of Great Stellated Dodecahedron (rc). 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 Ridge Length of Great Stellated Dodecahedron?
In this formula, Ridge Length of Great Stellated Dodecahedron uses Circumradius of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*Edge Length of Great Stellated Dodecahedron
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
  • Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)
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