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 Volume of Dodecahedron given Insphere Radius?
Volume of Dodecahedron given Insphere Radius calculator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3 to calculate the Volume of Dodecahedron, The Volume of Dodecahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the insphere radius of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.
How to calculate Volume of Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (r_{i}) and hit the calculate button. Here is how the Volume of Dodecahedron given Insphere Radius calculation can be explained with given input values -> 7387.437 = 1/4*(15+(7*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^3.