3Dimensional Geometry

Is a Soccer ball just a ball?

Even though this question might seem simple, a soccer ball isn’t a “ball”, as many people think. 

As crazy as it may sound, “A soccer is a Polyhedron”.

Polyhedron

A polyhedron is a three-dimensional shape with flat faces, straight edges, and sharp corners (vertices). The term “polyhedron” derives from the Greek words poly, meaning “many,” and hedron, meaning “surface.” When many flat surfaces are joined together, a polyhedron is formed. The names of these shapes are based on their faces, which are typically polygons.

It’s a truncated, 32-sided icosahedron with both pentagonal and hexagonal surfaces. It has 60 vertices and is one of the least known and most widely used shapes in the entire world. This is the geometry of soccer.

It has 20 hexagons and 12 pentagons on it.

A short video summarises this:

Platonic Solids

Platonic solids are three-dimensional geometrical objects that have been studied for millennia due to their symmetry and beauty. Euclid, a Greek Mathematician proved that there are exactly five such solids.

They are a tetrahedron, a cube, an octahedron, a dodecahedron, and an icosahedron.

Regular polygons are those with all of their sides equal. Since a Regular Polygon has equal sides, it also has equal angles.

Number of sides ‘n’Regular Polygon
3Equilateral Triangle
4Square
5Pentagon
6Hexagon

and so on…

A Platonic solid is a three-dimensional shape, each face is a regular polygon, and the same number of polygons intersect at each vertex.

There are only five Platonic solids exist.

1. Cube

  • The cube consists of 6 squares
  • Three squares meet at each vertex
  • 8 vertices
  • 12 edges

2. Tetrahedron

  • The Tetrahedron consists of 4 Equilateral triangles.
  • Three triangles meet at each vertex.
  • 4 Vertices
  • 6 Edges

3. Octahedron

  • The Octahedron consists of 8 triangles
  • 4 triangles meet at each vertex
  • 8 Faces
  • 6 Vertices
  • 12 Edges

4. Dodecahedron

  • The dodecahedron consists of 12 Pentagons.
  • 3 pentagons meet at each vertex
  • 20 Vertices
  • 30 Edges

    5. Icosahedron

    • The Icosahedron consists of 20 Equilateral triangles.
    • 5 triangles meet at each vertex
    • 12 Vertices
    • 30 Edges