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 Icosahedron given Insphere Radius?
Space Diagonal of Icosahedron given Insphere Radius calculator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to calculate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_{Space} symbol.
How to calculate Space Diagonal of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Space Diagonal of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (r_{i}) and hit the calculate button. Here is how the Space Diagonal of Icosahedron given Insphere Radius calculation can be explained with given input values -> 17.61772 = sqrt(10+(2*sqrt(5)))*(6*7)/(sqrt(3)*(3+sqrt(5))).