## Midsphere Radius of Dodecahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
rm = (3+sqrt(5))/2*dSpace/(sqrt(3)*(1+sqrt(5)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Midsphere Radius of Dodecahedron - (Measured in Meter) - The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.
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
rm = (3+sqrt(5))/2*dSpace/(sqrt(3)*(1+sqrt(5))) --> (3+sqrt(5))/2*28/(sqrt(3)*(1+sqrt(5)))
Evaluating ... ...
rm = 13.078413025478
STEP 3: Convert Result to Output's Unit
13.078413025478 Meter --> No Conversion Required
13.078413025478 13.07841 Meter <-- Midsphere Radius of Dodecahedron
(Calculation completed in 00.003 seconds)
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## < 12 Midsphere Radius of Dodecahedron Calculators

Midsphere Radius of Dodecahedron given Surface to Volume Ratio
Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
Midsphere Radius of Dodecahedron given Lateral Surface Area
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Midsphere Radius of Dodecahedron given Total Surface Area
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Midsphere Radius of Dodecahedron given Face Area
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5))))
Midsphere Radius of Dodecahedron given Space Diagonal
Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
Midsphere Radius of Dodecahedron given Volume
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Midsphere Radius of Dodecahedron given Face Diagonal
Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5))
Midsphere Radius of Dodecahedron given Face Perimeter
Midsphere Radius of Dodecahedron = (3+sqrt(5))/20*Face Perimeter of Dodecahedron
Midsphere Radius of Dodecahedron given Perimeter
Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron

## Midsphere Radius of Dodecahedron given Space Diagonal Formula

Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
rm = (3+sqrt(5))/2*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 Midsphere Radius of Dodecahedron given Space Diagonal?

Midsphere Radius of Dodecahedron given Space Diagonal calculator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))) to calculate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Space Diagonal formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using space diagonal of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Dodecahedron given Space Diagonal using this online calculator? To use this online calculator for Midsphere Radius of Dodecahedron given Space Diagonal, enter Space Diagonal of Dodecahedron (dSpace) and hit the calculate button. Here is how the Midsphere Radius of Dodecahedron given Space Diagonal calculation can be explained with given input values -> 13.07841 = (3+sqrt(5))/2*28/(sqrt(3)*(1+sqrt(5))).

### FAQ

What is Midsphere Radius of Dodecahedron given Space Diagonal?
The Midsphere Radius of Dodecahedron given Space Diagonal formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using space diagonal of Dodecahedron and is represented as rm = (3+sqrt(5))/2*dSpace/(sqrt(3)*(1+sqrt(5))) or Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*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 Midsphere Radius of Dodecahedron given Space Diagonal?
The Midsphere Radius of Dodecahedron given Space Diagonal formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using space diagonal of Dodecahedron is calculated using Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). To calculate Midsphere Radius 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 Midsphere Radius of Dodecahedron?
In this formula, Midsphere Radius of Dodecahedron uses Space Diagonal of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5))))
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5))
• Midsphere Radius of Dodecahedron = (3+sqrt(5))/20*Face Perimeter of Dodecahedron