3D Visualisation

1D, 2D and 3D objects Length, Breadth and Height are dimensions. For example, a line

has one dimension (length), a square has two dimensions (length and breadth), and a cube has three dimensions (length, breadth and height).

Therefore,

1D = 1 Dimension (line)

2D = 2 Dimensions (square)

3D = 3 Dimensions (cube)

Some examples of 3D objects

Pyramids of Egypt (Pyramid)

Rubik's Cube (Cube)

Basket Ball (Sphere)

Euler’s Formula ‘Leonhard Euler’ was a pioneering Swiss mathematician and physicist.

He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He had invented a formula (popularly known as the Euler's formula):-

V - E + F = 2

Where, V = number of vertices, E = number of edges & F = number of faces

For Example, 1. Tetrahedron :- V = 4, E = 6, F = 4 & Therefore, 4 - 6 + 4 = 2

2. Cube :- V = 8, E = 12, F = 6 & Therefore, 8 - 12 + 6 = 2

Polyhedrons A Polyhedron is simply a three-dimensional solid which consists of a

collection of polygons, usually joined at their edges.

Net of a 3D Object The figure drawn on a 2D paper which when folded forms the 3D object is called as the net of a 3D shape.

For Example,

Prisms and Pyramids• A prism is a polyhedron, with two parallel faces called bases. The

other faces are always parallelograms. The prism is named by the shape of its base.

•  A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. It is a conic solid with polygonal base

Views of 3D Figures

There are mainly 3 views of a 3D figure :-

1.Top View2. Side View3.Front View

By:- Akshay Painjane