Ridge 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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✖Ridge Length of Small Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Small Stellated Dodecahedron.ⓘ Ridge Length of Small Stellated Dodecahedron given Circumradius [l_Ridge]

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Ridge Length of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))
l_Ridge = ((1+sqrt(5))/2)*((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

Ridge Length of Small Stellated Dodecahedron - (Measured in Meter) - Ridge Length of Small Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex 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_Ridge = ((1+sqrt(5))/2)*((4*r_c)/(sqrt(50+22*sqrt(5)))) --> ((1+sqrt(5))/2)*((4*25)/(sqrt(50+22*sqrt(5))))

Evaluating ... ...

l_Ridge = 16.2459848116453

STEP 3: Convert Result to Output's Unit

16.2459848116453 Meter --> No Conversion Required

FINAL ANSWER

16.2459848116453 ≈ 16.24598 Meter <-- Ridge Length of Small Stellated Dodecahedron

(Calculation completed in 00.004 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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< Ridge Length of Small Stellated Dodecahedron Calculators

Ridge Length of Small Stellated Dodecahedron given Pyramidal Height

LaTeX Go Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))

Ridge Length of Small Stellated Dodecahedron given Circumradius

LaTeX Go Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))

Ridge Length of Small Stellated Dodecahedron given Pentagram Chord

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

Ridge Length of Small Stellated Dodecahedron

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

Ridge Length of Small Stellated Dodecahedron given Circumradius Formula

LaTeX Go

Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))
l_Ridge = ((1+sqrt(5))/2)*((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 Ridge Length of Small Stellated Dodecahedron given Circumradius?

Ridge Length of Small Stellated Dodecahedron given Circumradius calculator uses Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))) to calculate the Ridge Length of Small Stellated Dodecahedron, Ridge Length of Small 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 Small Stellated Dodecahedron, calculated using its circumradius. Ridge Length of Small Stellated Dodecahedron is denoted by l_Ridge symbol.

How to calculate Ridge Length of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Ridge Length of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Ridge Length of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 16.24598 = ((1+sqrt(5))/2)*((4*25)/(sqrt(50+22*sqrt(5)))).

FAQ

What is Ridge Length of Small Stellated Dodecahedron given Circumradius?

Ridge Length of Small 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 Small Stellated Dodecahedron, calculated using its circumradius and is represented as l_Ridge = ((1+sqrt(5))/2)*((4*r_c)/(sqrt(50+22*sqrt(5)))) or Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((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 Ridge Length of Small Stellated Dodecahedron given Circumradius?

Ridge Length of Small 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 Small Stellated Dodecahedron, calculated using its circumradius is calculated using Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))). To calculate Ridge 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 Ridge Length of Small Stellated Dodecahedron?

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

Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Small Stellated Dodecahedron
Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
Ridge Length of Small Stellated Dodecahedron = ((1+sqrt(5))/2)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))

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