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Circumsphere Radius of Dodecahedron Calculator

Formula

The formula to calculate the Circumsphere Radius of Dodecahedron is:

$rc = \frac{\sqrt{3} \cdot (1 + \sqrt{5}) \cdot le}{4}$

Definition

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere. 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.

Example Calculation

Let's assume the following values:

Edge Length = 10 Meters

Using the formula:

$rc = \frac{\sqrt{3} \cdot (1 + \sqrt{5}) \cdot 10}{4} = 14.0125853844407$

The Circumsphere Radius is 14.0125853844407 Meters.

Conversion Chart

Edge Length (Meters)	Circumsphere Radius (Meters)
9	12.611326845996661
9.5	13.311956115218697
10	14.012585384440735
10.5	14.713214653662771
11	15.413843922884809