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 Diagonal of Dodecahedron given Total Surface Area?
Face Diagonal of Dodecahedron given Total Surface Area calculator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))) to calculate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Total Surface Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using total surface area of Dodecahedron. Face Diagonal of Dodecahedron is denoted by dFace symbol.
How to calculate Face Diagonal of Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Face Diagonal of Dodecahedron given Total Surface Area, enter Total Surface Area of Dodecahedron (TSA) and hit the calculate button. Here is how the Face Diagonal of Dodecahedron given Total Surface Area calculation can be explained with given input values -> 16.31857 = (1+sqrt(5))/2*sqrt(2100/(3*sqrt(25+(10*sqrt(5))))).