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 Edge Length of Dodecahedron given Circumsphere Radius?
Edge Length of Dodecahedron given Circumsphere Radius calculator uses Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) to calculate the Edge Length of Dodecahedron, Edge Length of Dodecahedron given Circumsphere Radius formula is defined as the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron, and calculated using the circumsphere radius of the Dodecahedron. Edge Length of Dodecahedron is denoted by l_{e} symbol.
How to calculate Edge Length of Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Edge Length of Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Dodecahedron (r_{c}) and hit the calculate button. Here is how the Edge Length of Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 9.991019 = (4*14)/(sqrt(3)*(1+sqrt(5))).