student presentation on Solid shapes

Class VIII     Visualising solid shapes

This blog is made by student of class VIII C (Prerana school)

Introduction

We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height.

In the world around us, there are many three-dimensional geometric shapes

Three-dimensional shapes whose faces are polygons are called polyhedrl. There are two special types of polyhedra: prisms and pyramids.

Polyhedra

A die is in the shape of a cube.

A portable DVD player is in the shape of a rectangular prism.

A soccer ball is in the shape of a truncated icosahedron. These shapes are all examples of polyhedra.

A three-dimensional shape whose faces are polygons is known as a polyhedron. This term comes from the Greek words poly, which means "many," and hedron, which means "face." So, quite literally, a polyhedron is a three-dimensional object with many faces. 

The faces of a cube are squares.

The faces of rectangular prism are rectangles.

The faces of a truncated icosahedron are pentagons and hexagons — there are some of each.

The other parts of a polyhedron are its edges, the line segments along which two faces intersect, and its vertices, the points at which three or more faces meet. 

As you already know that F + V - E = 2, is known as Euler’s formula. Here  is some interesting facts about that formula.

Euler's Theorem actually played a role in a notable discovery. In some chemistry experiments, a group of researchers believed that they had found a new molecule with the exact weight of 60 carbon atoms. Although they couldn't see this molecule, they speculated that its shape was a truncated icosahedron — a "soccer ball" in which 60 carbon atoms (vertices) were joined together by 90 bonds (edges). From Euler's Theorem, they then knew that the atoms must be arranged to form a spherical soccer ball with 32 faces, some of them hexagons and some pentagons.

Platonic Solids

There are five special polyhedra — known collectively as the Platonic solids— that are different from all the others. 

What makes the Platonic solids special? Well, two things, actually. 

1. They are the only polyhedra whose faces are all exactly the same. Every face is identical to every other face. For instance, a cube is a Platonic solid because all six of its faces are congruent squares. 

2. The same number of faces meet at each vertex. Every vertex has the same number of adjacent faces as every other vertex. For example, three equilateral triangles meet at each vertex of a tetrahedron. 

No other polyhedra satisfy both of these conditions. Consider a pentagonal prism. It satisfies the second condition because three faces meet at each vertex, but it violates the first condition because the faces are not identical — some are pentagons and some are rectangles.

Here are the net of all platonic solids, using it you can make model of it

1.     Cube

2.     Tetrahedron

3.     Octahedron

4.     Dodecahedron
5.     Icosahedron