Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord Calculator

✖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.ⓘ Pentagram Chord of Great Stellated Dodecahedron [l_c(Pentagram)]

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✖Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.ⓘ Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord [h_Pyramid]

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Formula

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Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord

Formula

`"h"_{"Pyramid"} = (sqrt(3)*(3+sqrt(5)))/6*"l"_{"c(Pentagram)"}/(2+sqrt(5))`

Example

`"14.98653m"=(sqrt(3)*(3+sqrt(5)))/6*"42m"/(2+sqrt(5))`

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Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
h_Pyramid = (sqrt(3)*(3+sqrt(5)))/6*l_c(Pentagram)/(2+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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Great Stellated Dodecahedron: 42 Meter --> 42 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Pyramid = (sqrt(3)*(3+sqrt(5)))/6*l_c(Pentagram)/(2+sqrt(5)) --> (sqrt(3)*(3+sqrt(5)))/6*42/(2+sqrt(5))

Evaluating ... ...

h_Pyramid = 14.9865277704698

STEP 3: Convert Result to Output's Unit

14.9865277704698 Meter --> No Conversion Required

FINAL ANSWER

14.9865277704698 ≈ 14.98653 Meter <-- Pyramidal Height of Great Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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< 7 Pyramidal Height of Great Stellated Dodecahedron Calculators

Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area

Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))

Pyramidal Height of Great Stellated Dodecahedron given Volume

Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)

Pyramidal Height of Great Stellated Dodecahedron given Ridge Length

Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord

Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

Pyramidal Height of Great Stellated Dodecahedron given Surface to Volume Ratio

Go Pyramidal Height of Great Stellated Dodecahedron = (2*sqrt(3)*sqrt(5+(2*sqrt(5))))/SA:V of Great Stellated Dodecahedron

Pyramidal Height of Great Stellated Dodecahedron

Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Edge Length of Great Stellated Dodecahedron

Pyramidal Height of Great Stellated Dodecahedron given Circumradius

Go Pyramidal Height of Great Stellated Dodecahedron = (2*Circumradius of Great Stellated Dodecahedron)/3

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord Formula

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

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord calculator uses Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)) to calculate the Pyramidal Height of Great Stellated Dodecahedron, Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron, calculated using its pentagram chord. Pyramidal Height of Great Stellated Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 14.98653 = (sqrt(3)*(3+sqrt(5)))/6*42/(2+sqrt(5)).

FAQ

What is Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord?

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron, calculated using its pentagram chord and is represented as h_Pyramid = (sqrt(3)*(3+sqrt(5)))/6*l_c(Pentagram)/(2+sqrt(5)) or Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)). 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.

How to calculate Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord?

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron, calculated using its pentagram chord is calculated using Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)). To calculate Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord 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 Pyramidal Height of Great Stellated Dodecahedron?

In this formula, Pyramidal Height of Great Stellated Dodecahedron uses Pentagram Chord of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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