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Edge length of Great Dodecahedron given circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5)))
Sa = (4*rc)/(sqrt(10+2*sqrt(5)))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Circumradius - Circumradius is the radius of a circumsphere touching each of the polyhedron's or polygon's vertices. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Circumradius: 15 Meter --> 15 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Sa = (4*rc)/(sqrt(10+2*sqrt(5))) --> (4*15)/(sqrt(10+2*sqrt(5)))
Evaluating ... ...
Sa = 15.771933363574
STEP 3: Convert Result to Output's Unit
15.771933363574 Meter --> No Conversion Required
FINAL ANSWER
15.771933363574 Meter <-- Side A
(Calculation completed in 00.015 seconds)

6 Edge length of Great Dodecahedron Calculators

Edge length of Great Dodecahedron given surface to volume ratio
side_a = (15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)*Surface to Volume Ratio) Go
Edge length of Great Dodecahedron given surface area
side_a = sqrt(Surface Area/(15*(sqrt(5-2*sqrt(5))))) Go
Edge length of Great Dodecahedron given circumradius
side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5))) Go
Edge length of Great Dodecahedron given pyramid height
side_a = (6*Height)/(sqrt(3)*(3-sqrt(5))) Go
Edge length of Great Dodecahedron given volume
side_a = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3) Go
Edge length of Great Dodecahedron given ridge length
side_a = (2*Length)/(sqrt(5)-1) Go

Edge length of Great Dodecahedron given circumradius Formula

side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5)))
Sa = (4*rc)/(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 of Great Dodecahedron given circumradius?

Edge length of Great Dodecahedron given circumradius calculator uses side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5))) to calculate the Side A, Edge length of Great Dodecahedron given circumradius formula is defined as a straight line connecting two vertices of Great Dodecahedron. Side A and is denoted by Sa symbol.

How to calculate Edge length of Great Dodecahedron given circumradius using this online calculator? To use this online calculator for Edge length of Great Dodecahedron given circumradius, enter Circumradius (rc) and hit the calculate button. Here is how the Edge length of Great Dodecahedron given circumradius calculation can be explained with given input values -> 15.77193 = (4*15)/(sqrt(10+2*sqrt(5))).

FAQ

What is Edge length of Great Dodecahedron given circumradius?
Edge length of Great Dodecahedron given circumradius formula is defined as a straight line connecting two vertices of Great Dodecahedron and is represented as Sa = (4*rc)/(sqrt(10+2*sqrt(5))) or side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5))). Circumradius is the radius of a circumsphere touching each of the polyhedron's or polygon's vertices.
How to calculate Edge length of Great Dodecahedron given circumradius?
Edge length of Great Dodecahedron given circumradius formula is defined as a straight line connecting two vertices of Great Dodecahedron is calculated using side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5))). To calculate Edge length of Great Dodecahedron given circumradius, you need Circumradius (rc). With our tool, you need to enter the respective value for Circumradius 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 Side A?
In this formula, Side A uses Circumradius. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • side_a = (2*Length)/(sqrt(5)-1)
  • side_a = (4*Circumradius)/(sqrt(10+2*sqrt(5)))
  • side_a = (6*Height)/(sqrt(3)*(3-sqrt(5)))
  • side_a = sqrt(Surface Area/(15*(sqrt(5-2*sqrt(5)))))
  • side_a = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3)
  • side_a = (15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)*Surface to Volume Ratio)
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