Pyramidal Height of Small Stellated Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron
hPyramid = ((sqrt(25+10*sqrt(5)))/5)*le
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.
Edge Length of Small Stellated Dodecahedron - (Measured in Meter) - Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Small Stellated Dodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
hPyramid = ((sqrt(25+10*sqrt(5)))/5)*le --> ((sqrt(25+10*sqrt(5)))/5)*10
Evaluating ... ...
hPyramid = 13.7638192047117
STEP 3: Convert Result to Output's Unit
13.7638192047117 Meter --> No Conversion Required
FINAL ANSWER
13.7638192047117 13.76382 Meter <-- Pyramidal Height of Small Stellated Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

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Walchand College of Engineering (WCE), Sangli
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7 Pyramidal Height of Small Stellated Dodecahedron Calculators

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))
Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
Pyramidal Height of Small Stellated Dodecahedron given Circumradius
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 Volume
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
Pyramidal Height of Small Stellated Dodecahedron given Ridge Length
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
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
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 Formula

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

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?

Pyramidal Height of Small Stellated Dodecahedron calculator uses Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron to calculate the Pyramidal Height of Small Stellated Dodecahedron, Pyramidal Height of Small Stellated Dodecahedron formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron. Pyramidal Height of Small Stellated Dodecahedron is denoted by hPyramid symbol.

How to calculate Pyramidal Height of Small Stellated Dodecahedron using this online calculator? To use this online calculator for Pyramidal Height of Small Stellated Dodecahedron, enter Edge Length of Small Stellated Dodecahedron (le) and hit the calculate button. Here is how the Pyramidal Height of Small Stellated Dodecahedron calculation can be explained with given input values -> 13.76382 = ((sqrt(25+10*sqrt(5)))/5)*10.

FAQ

What is Pyramidal Height of Small Stellated Dodecahedron?
Pyramidal Height of Small Stellated Dodecahedron formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron and is represented as hPyramid = ((sqrt(25+10*sqrt(5)))/5)*le or Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron. Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.
How to calculate Pyramidal Height of Small Stellated Dodecahedron?
Pyramidal Height of Small Stellated Dodecahedron formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron is calculated using Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron. To calculate Pyramidal Height of Small Stellated Dodecahedron, you need Edge Length of Small Stellated Dodecahedron (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • 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 = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))
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