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))).