Polygons are the flat surface made up of line segments. The 3-D shapes made up of polygons are called polyhedron.
The solid shape who’s all the faces are not polygon are called non-polyhedron. i.e. it has one of the curved faces.
If the line segment formed by joining any two vertices of the polyhedron lies inside the figure then it is said to be a convex polyhedron.
Non-convex or Concave Polyhedron
If anyone or more line segments formed by joining any two vertices of the polyhedron lie outside the figure then it is said to be a non-convex polyhedron.
If all the faces of a polyhedron are regular polygons and its same number of faces meets at each vertex then it is called regular polyhedron.
The polyhedron which is not regular is called non-regular polyhedron. Its vertices are not made by the same number of faces.
In this figure, 4 faces meet at the top point and 3 faces meet at all the bottom points.
If the top and bottom of a polyhedron are a congruent polygon and its lateral faces are parallelogram in shape, then it is said to be a prism.
If the base of a polyhedron is the polygon and its lateral faces are triangular in shape with a common vertex, then it is said to be a pyramid.
Hollow hexagonal Prism: Formed by joining two hexagons and six rectangles as shown below:
Hollow Cylinder: A cylinder is made by rotating a rectangle around either its length or breadth as shown below.
|Solid||Number of Faces||Number of Edges||Number of Vertices|
Euler’s formula shows the relationship between edges, faces and vertices of a polyhedron.
Every polyhedron will satisfy the criterion F + V – E = 2,
Where F is the number of faces of the polyhedron, V is the vertices of the polyhedron and E is the number of edges of the polyhedron.
Using Euler’s formula, find the number of faces if the number of vertices is 6 and the number of edges is 12.
Given, V = 6 and E = 12.
We know Euler’s formula, F + V – E = 2
So, F + 6 – 12 = 2.
Hence, F = 8.