Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length Calculator

✖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 [l_Ridge]

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✖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.ⓘ Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length [r_c]

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Formula

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Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length

Formula

`"r"_{"c"} = ((sqrt(50+22*sqrt(5)))/4)*((2*"l"_{"Ridge"})/(1+sqrt(5)))`

Example

`"24.62147m"=((sqrt(50+22*sqrt(5)))/4)*((2*"16m")/(1+sqrt(5)))`

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Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Ridge Length of Small Stellated Dodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = ((sqrt(50+22*sqrt(5)))/4)*((2*l_Ridge)/(1+sqrt(5))) --> ((sqrt(50+22*sqrt(5)))/4)*((2*16)/(1+sqrt(5)))

Evaluating ... ...

r_c = 24.621468297402

STEP 3: Convert Result to Output's Unit

24.621468297402 Meter --> No Conversion Required

FINAL ANSWER

24.621468297402 ≈ 24.62147 Meter <-- Circumradius of Small Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Small Stellated Dodecahedron » Circumsphere Radius of Small Stellated Dodecahedron » Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length

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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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< 7 Circumsphere Radius of Small Stellated Dodecahedron Calculators

Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))

Circumsphere Radius of Small Stellated Dodecahedron given Total Surface Area

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))

Circumsphere Radius of Small Stellated Dodecahedron given Pyramidal Height

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))

Circumsphere Radius of Small Stellated Dodecahedron given Volume

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length

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

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

Circumsphere Radius of Small Stellated Dodecahedron

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

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length Formula

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

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length calculator uses Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5))) to calculate the Circumradius of Small Stellated Dodecahedron, Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its ridge length. Circumradius of Small Stellated Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length using this online calculator? To use this online calculator for Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length, enter Ridge Length of Small Stellated Dodecahedron (l_Ridge) and hit the calculate button. Here is how the Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length calculation can be explained with given input values -> 24.62147 = ((sqrt(50+22*sqrt(5)))/4)*((2*16)/(1+sqrt(5))).

FAQ

What is Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length?

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its ridge length and is represented as r_c = ((sqrt(50+22*sqrt(5)))/4)*((2*l_Ridge)/(1+sqrt(5))) or Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5))). 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.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length?

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its ridge length is calculated using Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5))). To calculate Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length, you need Ridge Length of Small Stellated Dodecahedron (l_Ridge). With our tool, you need to enter the respective value for Ridge Length 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 Circumradius of Small Stellated Dodecahedron?

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

Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))

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