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 Insphere Radius of Dodecahedron given Surface to Volume Ratio?
Insphere Radius of Dodecahedron given Surface to Volume Ratio calculator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to calculate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using surface to volume ratio of Dodecahedron. Insphere Radius of Dodecahedron is denoted by ri symbol.
How to calculate Insphere Radius of Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Dodecahedron (RA/V) and hit the calculate button. Here is how the Insphere Radius of Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 10 = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).