Face Diagonal of Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
dFace = ((1+sqrt(5))/2)*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
Face Diagonal of Dodecahedron - (Measured in Meter) - The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.
Edge Length of Dodecahedron - (Measured in Meter) - Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Dodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dFace = ((1+sqrt(5))/2)*le --> ((1+sqrt(5))/2)*10
Evaluating ... ...
dFace = 16.1803398874989
STEP 3: Convert Result to Output's Unit
16.1803398874989 Meter --> No Conversion Required
FINAL ANSWER
16.1803398874989 16.18034 Meter <-- Face Diagonal of Dodecahedron
(Calculation completed in 00.007 seconds)

Credits

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Created by Nikhil
Mumbai University (DJSCE), Mumbai
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The National Institute of Engineering (NIE), Mysuru
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12 Face Diagonal of Dodecahedron Calculators

Face Diagonal of Dodecahedron given Surface to Volume Ratio
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron)
Face Diagonal of Dodecahedron given Lateral Surface Area
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Total Surface Area
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Face Area
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Insphere Radius
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Face Diagonal of Dodecahedron given Volume
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron given Midsphere Radius
​ Go Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius of Dodecahedron
Face Diagonal of Dodecahedron given Circumsphere Radius
​ Go Face Diagonal of Dodecahedron = 2/sqrt(3)*Circumsphere Radius of Dodecahedron
Face Diagonal of Dodecahedron given Face Perimeter
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/10*Face Perimeter of Dodecahedron
Face Diagonal of Dodecahedron
​ Go Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
Face Diagonal of Dodecahedron given Perimeter
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/60*Perimeter of Dodecahedron
Face Diagonal of Dodecahedron given Space Diagonal
​ Go Face Diagonal of Dodecahedron = Space Diagonal of Dodecahedron/sqrt(3)

6 Diagonal of Dodecahedron Calculators

Space Diagonal of Dodecahedron given Lateral Surface Area
​ Go Space Diagonal of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Total Surface Area
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Insphere Radius
​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Space Diagonal of Dodecahedron
​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
Space Diagonal of Dodecahedron given Perimeter
​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/60
Face Diagonal of Dodecahedron
​ Go Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron

Face Diagonal of Dodecahedron Formula

Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
dFace = ((1+sqrt(5))/2)*le

What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Face Diagonal of Dodecahedron?

Face Diagonal of Dodecahedron calculator uses Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron to calculate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. Face Diagonal of Dodecahedron is denoted by dFace symbol.

How to calculate Face Diagonal of Dodecahedron using this online calculator? To use this online calculator for Face Diagonal of Dodecahedron, enter Edge Length of Dodecahedron (le) and hit the calculate button. Here is how the Face Diagonal of Dodecahedron calculation can be explained with given input values -> 16.18034 = ((1+sqrt(5))/2)*10.

FAQ

What is Face Diagonal of Dodecahedron?
The Face Diagonal of Dodecahedron formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron and is represented as dFace = ((1+sqrt(5))/2)*le or Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron. Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
How to calculate Face Diagonal of Dodecahedron?
The Face Diagonal of Dodecahedron formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron is calculated using Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron. To calculate Face Diagonal of Dodecahedron, you need Edge Length of Dodecahedron (le). With our tool, you need to enter the respective value for Edge Length of 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 Face Diagonal of Dodecahedron?
In this formula, Face Diagonal of Dodecahedron uses Edge Length of Dodecahedron. We can use 13 other way(s) to calculate the same, which is/are as follows -
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
  • Face Diagonal of Dodecahedron = 2/sqrt(3)*Circumsphere Radius of Dodecahedron
  • Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/10*Face Perimeter of Dodecahedron
  • Face Diagonal of Dodecahedron = Space Diagonal of Dodecahedron/sqrt(3)
  • Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius of Dodecahedron
  • Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron)
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/60*Perimeter of Dodecahedron
  • Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
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