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 Midsphere Radius?
Space Diagonal of Dodecahedron given Midsphere Radius calculator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) to calculate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Midsphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using midsphere radius of Dodecahedron. Space Diagonal of Dodecahedron is denoted by dSpace symbol.
How to calculate Space Diagonal of Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Space Diagonal of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (rm) and hit the calculate button. Here is how the Space Diagonal of Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 27.83212 = sqrt(3)*(1+sqrt(5))*(2*13)/(3+sqrt(5)).