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Edge length of Great Icosahedron given circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5)))
Sa = (4*rc)/(sqrt(50+22*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(50+22*sqrt(5))) --> (4*15)/(sqrt(50+22*sqrt(5)))
Evaluating ... ...
Sa = 6.02434247658682
STEP 3: Convert Result to Output's Unit
6.02434247658682 Meter --> No Conversion Required
FINAL ANSWER
6.02434247658682 Meter <-- Side A
(Calculation completed in 00.015 seconds)

7 Edge length of Great Icosahedron Calculators

Edge length of Great Icosahedron given surface to volume ratio
side_a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*Surface to Volume Ratio) Go
Edge length of Great Icosahedron given surface area
side_a = sqrt(Surface Area/(3*sqrt(3)*(5+4*sqrt(5)))) Go
Edge length of Great Icosahedron given ridge length 2
side_a = (10*Ridge Length 2)/(sqrt(2)*(5+3*sqrt(5))) Go
Edge length of Great Icosahedron given circumradius
side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5))) Go
Edge length of Great Icosahedron given volume
side_a = ((4*Volume)/(25+9*sqrt(5)))^(1/3) Go
Edge length of Great Icosahedron given ridge length 1
side_a = (2*Ridge Length 1)/(1+sqrt(5)) Go
Edge length of Great Icosahedron given ridge length 3
side_a = (5*Ridge Length 3)/sqrt(10) Go

Edge length of Great Icosahedron given circumradius Formula

side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5)))
Sa = (4*rc)/(sqrt(50+22*sqrt(5)))

What is Great Icosahedron?

In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra, with Schläfli symbol {3, ​⁵⁄₂} and Coxeter–Dynkin diagram of. It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.

How to Calculate Edge length of Great Icosahedron given circumradius?

Edge length of Great Icosahedron given circumradius calculator uses side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5))) to calculate the Side A, Edge length of Great Icosahedron given circumradius formula is defined as a straight line connecting two vertices of Great Icosahedron. Side A and is denoted by Sa symbol.

How to calculate Edge length of Great Icosahedron given circumradius using this online calculator? To use this online calculator for Edge length of Great Icosahedron given circumradius, enter Circumradius (rc) and hit the calculate button. Here is how the Edge length of Great Icosahedron given circumradius calculation can be explained with given input values -> 6.024342 = (4*15)/(sqrt(50+22*sqrt(5))).

FAQ

What is Edge length of Great Icosahedron given circumradius?
Edge length of Great Icosahedron given circumradius formula is defined as a straight line connecting two vertices of Great Icosahedron and is represented as Sa = (4*rc)/(sqrt(50+22*sqrt(5))) or side_a = (4*Circumradius)/(sqrt(50+22*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 Icosahedron given circumradius?
Edge length of Great Icosahedron given circumradius formula is defined as a straight line connecting two vertices of Great Icosahedron is calculated using side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5))). To calculate Edge length of Great Icosahedron 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 7 other way(s) to calculate the same, which is/are as follows -
  • side_a = (2*Ridge Length 1)/(1+sqrt(5))
  • side_a = (10*Ridge Length 2)/(sqrt(2)*(5+3*sqrt(5)))
  • side_a = (5*Ridge Length 3)/sqrt(10)
  • side_a = (4*Circumradius)/(sqrt(50+22*sqrt(5)))
  • side_a = sqrt(Surface Area/(3*sqrt(3)*(5+4*sqrt(5))))
  • side_a = ((4*Volume)/(25+9*sqrt(5)))^(1/3)
  • side_a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*Surface to Volume Ratio)
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