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 Icosahedron given Space Diagonal?
Insphere Radius of Icosahedron given Space Diagonal calculator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))) to calculate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the space diagonal of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_{i} symbol.
How to calculate Insphere Radius of Icosahedron given Space Diagonal using this online calculator? To use this online calculator for Insphere Radius of Icosahedron given Space Diagonal, enter Space Diagonal of Icosahedron (d_{Space}) and hit the calculate button. Here is how the Insphere Radius of Icosahedron given Space Diagonal calculation can be explained with given input values -> 7.549217 = (sqrt(3)*(3+sqrt(5)))/12*(2*19)/sqrt(10+(2*sqrt(5))).