Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
lc(Pentagram) = (2+sqrt(5))*(6*hPyramid)/(sqrt(3)*(3+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
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.
Pyramidal Height of Great Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Pyramidal Height of Great Stellated Dodecahedron: 15 Meter --> 15 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
lc(Pentagram) = (2+sqrt(5))*(6*hPyramid)/(sqrt(3)*(3+sqrt(5))) --> (2+sqrt(5))*(6*15)/(sqrt(3)*(3+sqrt(5)))
Evaluating ... ...
lc(Pentagram) = 42.0377561533222
STEP 3: Convert Result to Output's Unit
42.0377561533222 Meter --> No Conversion Required
FINAL ANSWER
42.0377561533222 42.03776 Meter <-- Pentagram Chord of Great Stellated Dodecahedron
(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli
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7 Pentagram Chord of Great Stellated Dodecahedron Calculators

Pentagram Chord of Great Stellated Dodecahedron given Total Surface Area
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)
Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Pentagram Chord of Great Stellated Dodecahedron given Circumradius
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Pentagram Chord of Great Stellated Dodecahedron given Volume
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
Pentagram Chord of Great Stellated Dodecahedron given Ridge Length
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Pentagram Chord of Great Stellated Dodecahedron
Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*Edge Length of Great Stellated Dodecahedron

Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height Formula

Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
lc(Pentagram) = (2+sqrt(5))*(6*hPyramid)/(sqrt(3)*(3+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 Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height?

Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height calculator uses Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Pentagram Chord of Great Stellated Dodecahedron, Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its pyramidal height. Pentagram Chord of Great Stellated Dodecahedron is denoted by lc(Pentagram) symbol.

How to calculate Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Stellated Dodecahedron (hPyramid) and hit the calculate button. Here is how the Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 42.03776 = (2+sqrt(5))*(6*15)/(sqrt(3)*(3+sqrt(5))).

FAQ

What is Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height?
Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its pyramidal height and is represented as lc(Pentagram) = (2+sqrt(5))*(6*hPyramid)/(sqrt(3)*(3+sqrt(5))) or Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))). Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.
How to calculate Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height?
Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its pyramidal height is calculated using Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))). To calculate Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height, you need Pyramidal Height of Great Stellated Dodecahedron (hPyramid). With our tool, you need to enter the respective value for Pyramidal Height 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 Pentagram Chord of Great Stellated Dodecahedron?
In this formula, Pentagram Chord of Great Stellated Dodecahedron uses Pyramidal Height of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*Edge Length of Great Stellated Dodecahedron
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
  • Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)
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