Pyramidal Height of Small Stellated Dodecahedron given Circumradius Calculator

✖Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.ⓘ Circumradius of Small Stellated Dodecahedron [r_c]

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

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Pyramidal Height of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))
h_Pyramid = ((sqrt(25+10*sqrt(5)))/5)*((4*r_c)/(sqrt(50+22*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 Small Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.
Circumradius of Small Stellated Dodecahedron - (Measured in Meter) - Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Small Stellated Dodecahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Pyramid = ((sqrt(25+10*sqrt(5)))/5)*((4*r_c)/(sqrt(50+22*sqrt(5)))) --> ((sqrt(25+10*sqrt(5)))/5)*((4*25)/(sqrt(50+22*sqrt(5))))

Evaluating ... ...

h_Pyramid = 13.8196601125011

STEP 3: Convert Result to Output's Unit

13.8196601125011 Meter --> No Conversion Required

FINAL ANSWER

13.8196601125011 ≈ 13.81966 Meter <-- Pyramidal Height of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< Pyramidal Height of Small Stellated Dodecahedron Calculators

Pyramidal Height of Small Stellated Dodecahedron given Circumradius

LaTeX Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))

Pyramidal Height of Small Stellated Dodecahedron given Ridge Length

LaTeX Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))

Pyramidal Height of Small Stellated Dodecahedron given Pentagram Chord

LaTeX Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

Pyramidal Height of Small Stellated Dodecahedron

LaTeX Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron

Pyramidal Height of Small Stellated Dodecahedron given Circumradius Formula

LaTeX Go

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

How to Calculate Pyramidal Height of Small Stellated Dodecahedron given Circumradius?

Pyramidal Height of Small Stellated Dodecahedron given Circumradius calculator uses Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))) to calculate the Pyramidal Height of Small Stellated Dodecahedron, Pyramidal Height of Small Stellated Dodecahedron given Circumradius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its circumradius. Pyramidal Height of Small Stellated Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Pyramidal Height of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Pyramidal Height of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 13.81966 = ((sqrt(25+10*sqrt(5)))/5)*((4*25)/(sqrt(50+22*sqrt(5)))).

FAQ

What is Pyramidal Height of Small Stellated Dodecahedron given Circumradius?

Pyramidal Height of Small Stellated Dodecahedron given Circumradius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its circumradius and is represented as h_Pyramid = ((sqrt(25+10*sqrt(5)))/5)*((4*r_c)/(sqrt(50+22*sqrt(5)))) or Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))). Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.

How to calculate Pyramidal Height of Small Stellated Dodecahedron given Circumradius?

Pyramidal Height of Small Stellated Dodecahedron given Circumradius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its circumradius is calculated using Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5)))). To calculate Pyramidal Height of Small Stellated Dodecahedron given Circumradius, you need Circumradius of Small Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius of Small 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 Small Stellated Dodecahedron?

In this formula, Pyramidal Height of Small Stellated Dodecahedron uses Circumradius of Small Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron
Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))
Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

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