Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord Calculator

✖Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.ⓘ Pentagram Chord of Great Stellated Dodecahedron [l_c(Pentagram)]

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✖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.ⓘ Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord [r_c]

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Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
r_c = (sqrt(3)*(3+sqrt(5)))/4*l_c(Pentagram)/(2+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 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.
Pentagram Chord of Great Stellated Dodecahedron - (Measured in Meter) - Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Great Stellated Dodecahedron: 42 Meter --> 42 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (sqrt(3)*(3+sqrt(5)))/4*l_c(Pentagram)/(2+sqrt(5)) --> (sqrt(3)*(3+sqrt(5)))/4*42/(2+sqrt(5))

Evaluating ... ...

r_c = 22.4797916557047

STEP 3: Convert Result to Output's Unit

22.4797916557047 Meter --> No Conversion Required

FINAL ANSWER

22.4797916557047 ≈ 22.47979 Meter <-- Circumradius of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< Radius of Great Stellated Dodecahedron Calculators

Circumsphere Radius of Great Stellated Dodecahedron given Ridge Length

LaTeX Go Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord

LaTeX Go Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

Circumsphere Radius of Great Stellated Dodecahedron

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

Circumsphere Radius of Great Stellated Dodecahedron given Pyramidal Height

LaTeX Go Circumradius of Great Stellated Dodecahedron = (3*Pyramidal Height of Great Stellated Dodecahedron)/2

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord Formula

LaTeX Go

Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
r_c = (sqrt(3)*(3+sqrt(5)))/4*l_c(Pentagram)/(2+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 Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord calculator uses Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)) to calculate the Circumradius of Great Stellated Dodecahedron, Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord. Circumradius of Great Stellated Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 22.47979 = (sqrt(3)*(3+sqrt(5)))/4*42/(2+sqrt(5)).

FAQ

What is Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord and is represented as r_c = (sqrt(3)*(3+sqrt(5)))/4*l_c(Pentagram)/(2+sqrt(5)) or Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)). Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.

How to calculate Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord is calculated using Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)). To calculate Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord 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 Circumradius of Great Stellated Dodecahedron?

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

Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron
Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Circumradius of Great Stellated Dodecahedron = (3*Pyramidal Height of Great Stellated Dodecahedron)/2

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