Perimeter of Dodecahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
P = (60*dSpace)/(sqrt(3)*(1+sqrt(5)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Perimeter of Dodecahedron - (Measured in Meter) - Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
Space Diagonal of Dodecahedron - (Measured in Meter) - The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Dodecahedron: 28 Meter --> 28 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (60*dSpace)/(sqrt(3)*(1+sqrt(5))) --> (60*28)/(sqrt(3)*(1+sqrt(5)))
Evaluating ... ...
P = 299.730555409396
STEP 3: Convert Result to Output's Unit
299.730555409396 Meter --> No Conversion Required
FINAL ANSWER
299.730555409396 299.7306 Meter <-- Perimeter of Dodecahedron
(Calculation completed in 00.003 seconds)

Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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12 Perimeter of Dodecahedron Calculators

Perimeter of Dodecahedron given Surface to Volume Ratio
Go Perimeter of Dodecahedron = (360*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
Perimeter of Dodecahedron given Lateral Surface Area
Go Perimeter of Dodecahedron = 30*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Perimeter of Dodecahedron given Total Surface Area
Go Perimeter of Dodecahedron = 30*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Perimeter of Dodecahedron given Face Area
Go Perimeter of Dodecahedron = 30*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
Perimeter of Dodecahedron given Circumsphere Radius
Go Perimeter of Dodecahedron = (120*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
Perimeter of Dodecahedron given Insphere Radius
Go Perimeter of Dodecahedron = (60*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
Perimeter of Dodecahedron given Space Diagonal
Go Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
Perimeter of Dodecahedron given Volume
Go Perimeter of Dodecahedron = 30*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Perimeter of Dodecahedron given Midsphere Radius
Go Perimeter of Dodecahedron = (120*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
Perimeter of Dodecahedron given Face Diagonal
Go Perimeter of Dodecahedron = (60*Face Diagonal of Dodecahedron)/(1+sqrt(5))
Perimeter of Dodecahedron given Face Perimeter
Go Perimeter of Dodecahedron = 6*Face Perimeter of Dodecahedron
Perimeter of Dodecahedron
Go Perimeter of Dodecahedron = 30*Edge Length of Dodecahedron

Perimeter of Dodecahedron given Space Diagonal Formula

Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
P = (60*dSpace)/(sqrt(3)*(1+sqrt(5)))

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 Perimeter of Dodecahedron given Space Diagonal?

Perimeter of Dodecahedron given Space Diagonal calculator uses Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) to calculate the Perimeter of Dodecahedron, The Perimeter of Dodecahedron given Space Diagonal formula is defined as the sum of the total distance around all the edges of the Dodecahedron and is calculated using the space diagonal of the Dodecahedron. Perimeter of Dodecahedron is denoted by P symbol.

How to calculate Perimeter of Dodecahedron given Space Diagonal using this online calculator? To use this online calculator for Perimeter of Dodecahedron given Space Diagonal, enter Space Diagonal of Dodecahedron (dSpace) and hit the calculate button. Here is how the Perimeter of Dodecahedron given Space Diagonal calculation can be explained with given input values -> 299.7306 = (60*28)/(sqrt(3)*(1+sqrt(5))).

FAQ

What is Perimeter of Dodecahedron given Space Diagonal?
The Perimeter of Dodecahedron given Space Diagonal formula is defined as the sum of the total distance around all the edges of the Dodecahedron and is calculated using the space diagonal of the Dodecahedron and is represented as P = (60*dSpace)/(sqrt(3)*(1+sqrt(5))) or Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.
How to calculate Perimeter of Dodecahedron given Space Diagonal?
The Perimeter of Dodecahedron given Space Diagonal formula is defined as the sum of the total distance around all the edges of the Dodecahedron and is calculated using the space diagonal of the Dodecahedron is calculated using Perimeter of Dodecahedron = (60*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). To calculate Perimeter of Dodecahedron given Space Diagonal, you need Space Diagonal of Dodecahedron (dSpace). With our tool, you need to enter the respective value for Space Diagonal 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 Perimeter of Dodecahedron?
In this formula, Perimeter of Dodecahedron uses Space Diagonal of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Perimeter of Dodecahedron = 30*Edge Length of Dodecahedron
  • Perimeter of Dodecahedron = (120*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
  • Perimeter of Dodecahedron = 30*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
  • Perimeter of Dodecahedron = (60*Face Diagonal of Dodecahedron)/(1+sqrt(5))
  • Perimeter of Dodecahedron = 6*Face Perimeter of Dodecahedron
  • Perimeter of Dodecahedron = (60*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
  • Perimeter of Dodecahedron = 30*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
  • Perimeter of Dodecahedron = (120*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
  • Perimeter of Dodecahedron = 30*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Perimeter of Dodecahedron = 30*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
  • Perimeter of Dodecahedron = (360*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
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