 POLYHEDRON.

Presentation on theme: "POLYHEDRON."— Presentation transcript:

POLYHEDRON

What do these have in common?
These are all polygons!

What do these have in common?
These are not polygons!

What do these have in common?
These are 3-D!

These are NOT polyhedron:

A polyhedron is: -three dimensional; -a closed figure;
-made up of flat surfaces which are polygons. What is a polyhedron? A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges. The word polyhedron is derived from the Greek poly (many) and the Indo-European hedron (seat).

All of the faces (sides) of a polyhedron are polygons.
The line segments where the faces intersect are called edges. The point where more than two faces intersect is called a vertex. vertex edges face

Some more polyhedra:

More polyhedron information Even more Polyhedron: More polyhedron!

There are only five regular polyhedra called the Platonic solids.
Crystals are real world examples of polyhedra. The salt you sprinkle on your food is a crystal in the shape of a cube. Math is everywhere! A polyhedron is said to be regular if its faces are made up of regular polygons. There are only five regular polyhedra called the Platonic solids.

More info In mathematics Plato's name is attached to the Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, and water. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

Pyramids

A pyramid . . . -is a polyhedron that has all faces except one
intersecting at one point; -has one polygon base; The sides that are not the base and intersect in a single point are triangles. -is named by the shape of its base. Triangular pyramid Pentagonal pyramid Hexagonal pyramid

PRISMS

A prism . . . -is a polyhedron with two congruent faces called
bases that are in parallel planes. The faces that are not bases are parallelograms, and are called lateral faces. -is named by the shape of its bases. E C A F B D

A plethora of polyhedra

A solid with a pair of circular bases is called a
cylinder. Is a cylinder a polyhedron?

A cone has a circular base and a vertex. Is a
cone a polyhedron?

Complete the table below.
letter Name of polyhedron Number of faces Number of edges Number of vertices A B C D E F G H

Completed table: A 5 9 6 B 4 C 12 8 D 7 15 10 E F 24 16 G H 21 14
letter Name of polyhedron Number of faces Number of edges Number of vertices A Triangular prism 5 9 6 B Triangular pyramid 4 C Square prism 12 8 D Pentagonal prism 7 15 10 E Hexagonal pyramid F Octagonal prism 24 16 G Rectangular pyramid H Septagonal prism 21 14 n = # sides on base Pyramid / prism n + 1 / n + 2 2n / 3n n + 1 / 2n

What is the relationship between the number
of vertices, faces and edges in a polyhedron? letter Name of polyhedron Number of faces Number of edges Number of vertices A Triangular prism 5 9 6 B Triangular pyramid 4 C Square prism 12 8 D Pentagonal prism 7 15 10 E Hexagonal pyramid F Octagonal prism 24 16 G Rectangular pyramid H Septagonal prism 21 14

More Euler information
What is the relationship between the number of vertices, faces and edges in a polyhedron? For any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. V + F = 2 + E This is called Euler’s formula. Click here for proofs of Euler’s formula More Euler information

Nets for many polyhedra
Interactive polyhedron Make some polyhedron models