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Circumradius of Great Stellated Dodecahedron given pyramid height Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5))))
rc = ((sqrt(3)*(3+sqrt(5)))/4)*((6*h)/(sqrt(3)*(3+sqrt(5))))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = ((sqrt(3)*(3+sqrt(5)))/4)*((6*h)/(sqrt(3)*(3+sqrt(5)))) --> ((sqrt(3)*(3+sqrt(5)))/4)*((6*12)/(sqrt(3)*(3+sqrt(5))))
Evaluating ... ...
rc = 18
STEP 3: Convert Result to Output's Unit
18 Meter --> No Conversion Required
FINAL ANSWER
18 Meter <-- Circumradius
(Calculation completed in 00.017 seconds)

7 Circumradius of Great Stellated Dodecahedron Calculators

Circumradius of Great Stellated Dodecahedron given surface to volume ratio
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(3+sqrt(5))*Surface to Volume Ratio)) Go
Circumradius of Great Stellated Dodecahedron given surface area
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5)))))) Go
Circumradius of Great Stellated Dodecahedron given pyramid height
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5)))) Go
Circumradius of Great Stellated Dodecahedron given volume
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(((4*Volume)/(5*(3+sqrt(5))))^(1/3)) Go
Circumradius of Great Stellated Dodecahedron given ridge length
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((2*Ridge Length 1)/(1+sqrt(5))) Go
Circumradius of Great Stellated Dodecahedron given pentagram chord
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(Chord Length/(2+sqrt(5))) Go
Circumradius of Great Stellated Dodecahedron given edge length
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*Side A Go

Circumradius of Great Stellated Dodecahedron given pyramid height Formula

circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5))))
rc = ((sqrt(3)*(3+sqrt(5)))/4)*((6*h)/(sqrt(3)*(3+sqrt(5))))

What is Great Stellated Dodecahedron?

In geometry, 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 Circumradius of Great Stellated Dodecahedron given pyramid height?

Circumradius of Great Stellated Dodecahedron given pyramid height calculator uses circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5)))) to calculate the Circumradius, Circumradius of Great Stellated Dodecahedron given pyramid height formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron. Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Great Stellated Dodecahedron given pyramid height using this online calculator? To use this online calculator for Circumradius of Great Stellated Dodecahedron given pyramid height, enter Height (h) and hit the calculate button. Here is how the Circumradius of Great Stellated Dodecahedron given pyramid height calculation can be explained with given input values -> 18 = ((sqrt(3)*(3+sqrt(5)))/4)*((6*12)/(sqrt(3)*(3+sqrt(5)))).

FAQ

What is Circumradius of Great Stellated Dodecahedron given pyramid height?
Circumradius of Great Stellated Dodecahedron given pyramid height formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron and is represented as rc = ((sqrt(3)*(3+sqrt(5)))/4)*((6*h)/(sqrt(3)*(3+sqrt(5)))) or circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5)))). Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Circumradius of Great Stellated Dodecahedron given pyramid height?
Circumradius of Great Stellated Dodecahedron given pyramid height formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron is calculated using circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5)))). To calculate Circumradius of Great Stellated Dodecahedron given pyramid height, you need Height (h). With our tool, you need to enter the respective value for Height 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?
In this formula, Circumradius uses Height. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*Side A
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((2*Ridge Length 1)/(1+sqrt(5)))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(Chord Length/(2+sqrt(5)))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5))))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5))))))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(((4*Volume)/(5*(3+sqrt(5))))^(1/3))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(3+sqrt(5))*Surface to Volume Ratio))
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