Space Diagonal of Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
dSpace = sqrt(3)*(1+sqrt(5))*ri/sqrt((25+(11*sqrt(5)))/10)
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
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.
Insphere Radius of Dodecahedron - (Measured in Meter) - Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Dodecahedron: 11 Meter --> 11 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = sqrt(3)*(1+sqrt(5))*ri/sqrt((25+(11*sqrt(5)))/10) --> sqrt(3)*(1+sqrt(5))*11/sqrt((25+(11*sqrt(5)))/10)
Evaluating ... ...
dSpace = 27.684988592026
STEP 3: Convert Result to Output's Unit
27.684988592026 Meter --> No Conversion Required
FINAL ANSWER
27.684988592026 27.68499 Meter <-- Space Diagonal of Dodecahedron
(Calculation completed in 00.004 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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Space Diagonal of Dodecahedron Calculators

Space Diagonal of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Face Area
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Volume
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Space Diagonal of Dodecahedron
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2

Space Diagonal of Dodecahedron given Insphere Radius Formula

​LaTeX ​Go
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
dSpace = sqrt(3)*(1+sqrt(5))*ri/sqrt((25+(11*sqrt(5)))/10)

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 Space Diagonal of Dodecahedron given Insphere Radius?

Space Diagonal of Dodecahedron given Insphere Radius calculator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10) to calculate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Insphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using insphere radius of Dodecahedron. Space Diagonal of Dodecahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Space Diagonal of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (ri) and hit the calculate button. Here is how the Space Diagonal of Dodecahedron given Insphere Radius calculation can be explained with given input values -> 27.68499 = sqrt(3)*(1+sqrt(5))*11/sqrt((25+(11*sqrt(5)))/10).

FAQ

What is Space Diagonal of Dodecahedron given Insphere Radius?
The Space Diagonal of Dodecahedron given Insphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using insphere radius of Dodecahedron and is represented as dSpace = sqrt(3)*(1+sqrt(5))*ri/sqrt((25+(11*sqrt(5)))/10) or Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
How to calculate Space Diagonal of Dodecahedron given Insphere Radius?
The Space Diagonal of Dodecahedron given Insphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using insphere radius of Dodecahedron is calculated using Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). To calculate Space Diagonal of Dodecahedron given Insphere Radius, you need Insphere Radius of Dodecahedron (ri). With our tool, you need to enter the respective value for Insphere Radius 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 Space Diagonal of Dodecahedron?
In this formula, Space Diagonal of Dodecahedron uses Insphere Radius of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
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