Visualising

solid shapes

Different type of shapes

3D Shapes

• Euler’s formula

Drawing a map

Content

Shapes

2D Shapes 3D Shapes

Different shapes

3D Shapes• Three-dimensional shapes have four

properties that set them apart from two-dimensional shapes: faces, vertices, edges and volume.

• These properties not only allow to determine whether the shape is two- or three-dimensional, but also which three-dimensional shape it is.

Face• The part of the shape

that is flat or curved.

• E.g. : Cube has six faces

Edge

• The part of the shape where two faces meet.

• E.g. : Cube has twelve edges

Vertex• The part of the

shape where three or four edges meet

• E.g. : Pyramid has four edges

Platonic Solid Picture Number

of Faces Shape of

Faces

Number of Faces at Each Vertex

Number of

Vertices

Number of Edges

Unfolded Polyhedron (Net)

Tetrahedron

4 Equilateral Triangle (3-sided)

3 4 6

Cube

6 Square (4-sided) 3 8 12

Octahedron

8 Equilateral Triangle (3-sided)

4 6 12

Dodecahedron

12 Regular

Pentagon (5-sided)

3 20 30

Icosahedron

20 Equilateral Triangle (3-sided)

5 12 30

ViewTop view

Front view

Side view

Object

Top view Front view Side view

Mapping • A map is a scaled graphic representation of a portion

of the earth's surface.

• The scale of the map permits the user to convert distance on the map to distance on the ground or vice versa.

• The ability to determine distance on a map, as well as on the earth's surface, is an important factor in planning and executing military missions.

• Distances Shown on the map are proportional to the actual distance on the ground.

• While drawing a map, we should take care about:

How much of actual distance is denoted by :1mm or 1cm in the map

• It can be : 1cm = 1 Kilometres or 10 Km or 100Km etc.

• This scale can vary from map to map but not within the map.

Polyhedron

Convex Concave Regular

Convex polyhedron A polyhedron is said to be convex if its surface (comprising its faces, edges and vertices) does not intersect itself and the line segment joining any two points of the polyhedron is contained in the interior or surface.

Concave polyhedron A polyhedron is said to be concave if its surface (comprising its faces, edges and vertices) intersect itself and the line segment joining any two points of the polyhedron is contained in the interior or surface.

Regular polyhedron A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex