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Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_edge = (4*Radius)/(sqrt(10+2*sqrt(5)))
a = (4*r)/(sqrt(10+2*sqrt(5)))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Radius: 18 Centimeter --> 0.18 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
a = (4*r)/(sqrt(10+2*sqrt(5))) --> (4*0.18)/(sqrt(10+2*sqrt(5)))
Evaluating ... ...
a = 0.189263200362888
STEP 3: Convert Result to Output's Unit
0.189263200362888 Meter --> No Conversion Required
FINAL ANSWER
0.189263200362888 Meter <-- Length of edge
(Calculation completed in 00.016 seconds)

6 Edge length of Great Dodecahedron Calculators

Edge length (a) of Great Dodecahedron given Surface-to-volume ratio (A/V)
length_edge = (15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)*surface to volume ratio) Go
Edge length (a) of Great Dodecahedron given Surface area (A)
length_edge = sqrt(Area/(15*(sqrt(5-2*sqrt(5))))) Go
Edge length (a) of Great Dodecahedron given Pyramid height (hp)
length_edge = (6*Height)/(sqrt(3)*(3-sqrt(5))) Go
Edge length (a) of Great Dodecahedron given Circumsphere radius (rc)
length_edge = (4*Radius)/(sqrt(10+2*sqrt(5))) Go
Edge length (a) of Great Dodecahedron given Volume (V)
length_edge = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3) Go
Edge length (a) of Great Dodecahedron given Ridge length (s)
length_edge = (2*length 1)/(sqrt(5)-1) Go

Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) Formula

length_edge = (4*Radius)/(sqrt(10+2*sqrt(5)))
a = (4*r)/(sqrt(10+2*sqrt(5)))

What is Great Dodecahedron ?

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Edge length (a) of Great Dodecahedron given Circumsphere radius (rc)?

Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) calculator uses length_edge = (4*Radius)/(sqrt(10+2*sqrt(5))) to calculate the Length of edge, The Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) formula is defined as a straight line connecting two vertices of Great Dodecahedron. Length of edge and is denoted by a symbol.

How to calculate Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) using this online calculator? To use this online calculator for Edge length (a) of Great Dodecahedron given Circumsphere radius (rc), enter Radius (r) and hit the calculate button. Here is how the Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) calculation can be explained with given input values -> 0.189263 = (4*0.18)/(sqrt(10+2*sqrt(5))).

FAQ

What is Edge length (a) of Great Dodecahedron given Circumsphere radius (rc)?
The Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) formula is defined as a straight line connecting two vertices of Great Dodecahedron and is represented as a = (4*r)/(sqrt(10+2*sqrt(5))) or length_edge = (4*Radius)/(sqrt(10+2*sqrt(5))). Radius is a radial line from the focus to any point of a curve.
How to calculate Edge length (a) of Great Dodecahedron given Circumsphere radius (rc)?
The Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) formula is defined as a straight line connecting two vertices of Great Dodecahedron is calculated using length_edge = (4*Radius)/(sqrt(10+2*sqrt(5))). To calculate Edge length (a) of Great Dodecahedron given Circumsphere radius (rc), you need Radius (r). With our tool, you need to enter the respective value for Radius 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 Length of edge?
In this formula, Length of edge uses Radius. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • length_edge = (2*length 1)/(sqrt(5)-1)
  • length_edge = (4*Radius)/(sqrt(10+2*sqrt(5)))
  • length_edge = (6*Height)/(sqrt(3)*(3-sqrt(5)))
  • length_edge = sqrt(Area/(15*(sqrt(5-2*sqrt(5)))))
  • length_edge = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3)
  • length_edge = (15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)*surface to volume ratio)
Where is the Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) calculator used?
Among many, Edge length (a) of Great Dodecahedron given Circumsphere radius (rc) calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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