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 Face Area of Dodecahedron given Circumsphere Radius?
Face Area of Dodecahedron given Circumsphere Radius calculator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to calculate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Circumsphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using circumsphere radius of Dodecahedron. Face Area of Dodecahedron is denoted by AFace symbol.
How to calculate Face Area of Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Face Area of Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Dodecahedron (rc) and hit the calculate button. Here is how the Face Area of Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 171.7388 = 1/4*sqrt(25+(10*sqrt(5)))*((4*14)/(sqrt(3)*(1+sqrt(5))))^2.