The work of the Greek polymath Plato has kept millions of people busy for millennia. A few among them have been mathematicians who have obsessed about Platonic solids, a class of geometric forms that are highly regular and are commonly found in nature.
Platonic solids, the first class of such shapes, are well known. They consist of five different shapes: tetrahedron, cube, octahedron, dodecahedron and icosahedron. They have four, six, eight, twelve and twenty faces, respectively.
What to learn from it?
Such mathematical discoveries don’t have immediate applications, but often many are found. For example, dome-shaped buildings are never circular in shape. Instead they are built like half-cut Goldberg polyhedra, consisting of many regular shapes that give more strength to the structure than using round-shaped construction material.
Also what i found intriguing was the beauty of these shapes their symmetric behaviour so i decided to build one of my own,you may not understand this till you look at one in real so lets get to it .
Understanding the structure
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of two types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron.
The 14 vertices of the rhombic dodecahedron are joined by 12 rhombi of the dimensions shown in the figure below
The rhombic dodecahedron can be built up by a placing six cubes on the faces of a seventh, in the configuration of a metal “jack” given below,
Joining the centers of the outer cubes with the vertices of the central cube then gives the rhombic dodecahedron.
Calculating the volume:
Making it Yourself
This is what i Made
