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 Surface to Volume Ratio of Dodecahedron given Perimeter?
Surface to Volume Ratio of Dodecahedron given Perimeter calculator uses Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+10*sqrt(5)))/(Perimeter of Dodecahedron*(15+7*sqrt(5))) to calculate the Surface to Volume Ratio of Dodecahedron, The Surface to Volume Ratio of Dodecahedron given Perimeter formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the perimeter of the Dodecahedron. Surface to Volume Ratio of Dodecahedron is denoted by R_{A/V} symbol.
How to calculate Surface to Volume Ratio of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Surface to Volume Ratio of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Surface to Volume Ratio of Dodecahedron given Perimeter calculation can be explained with given input values -> 0.269417 = (360*sqrt(25+10*sqrt(5)))/(300*(15+7*sqrt(5))).