Visualising Solid Shapes
Any shape that can be drawn on a plane is called a plane figure.
The plane figures are 2-D shapes, as they have two dimensions, i.e., length and breadth.
Any shape that occupies space is called a 3-D shape. These shapes have three dimensions, i.e., length, breadth and height.
3-D shapes look different from different positions, which are, front view, side view and top view.
A picture of a location is different from the map of the same location.
A picture is a detailed representation of the reality, whereas, a map shows the location of an object or a place in relation to other objects and places.
Different observers, if viewing from different positions, will give different descriptions of a picture. But this is not true for a map.
In a picture, perspective is important, whereas, in a map it is not important, as the map will remain the same, no matter in what position the observer is.
All three dimensional shapes have faces, edges and vertices.
The plane surface of a solid is called its face.
An edge of a solid is a line segment, along which two faces meet.
A point that is formed by three or more intersecting faces on a solid is called a vertex.
A polyhedron is a three dimensional solid, which consists of a collection of polygons, usually joined at their edges.
For any polyhedron, if
F = number of faces,
V = number of vertices, and
E = number of edges,
Then F + V – E = 2.
This relationship is called Euler’s formula.