1. Maksym Khomyshyn 3.C

2. Definition, characteristics and classification

3. Triangle Square Pentagon

4.  Name derives form Greek πολύς - much or many γωνία - corner or angle  Plain shape bound by a closed chain of a stright line segments.  Made of: Corners or vertex Edges or sides Body

5. Isn‘t a polygon Is a polygon

6. 6 vertexes 6 edges 1 body

7.  Number of sides  Convexity and types of non-convexity  Symmetry Regular Cyclic Equiangular Equilateral

9. α<180° α>180° ConvexConcave

11. Definition and characteristics

13.  Name derives form Greek πολύς – much or many έδρα - base, seat, or face  Three dimensional object bound by a finite number of polygons.

14.  3 dimensions: The Body  2 dimensions: A face  1 dimension: An edge  0 dimensions: A vertex

15. Face Edge Vertex Body

16.  Edges ◦ An edge joins just two vertices. ◦ An edge joins just two faces.  Euler characteristic ◦ The Euler characteristic χ relates the number of vertices V, edges E, and faces F of a polyhedron: X = V – E +F

17. Nature polyhedra around us

18. They are everywhere, but mostly we can not see them.

19. In chemistry Carbon nanotubes Metal nanoparticles Crystals

20. In Nature Cowpea virus body Honeycomb Starfruit or starfish Salt lake in Death Valley, CA Giant‘s Causeway in Ireland

21. Resources: Eric W. Weisstein - Polyhedron George W. Hart - Polyhedra from Symmetric Placement of Regular Polygons http://www.steelpillow.com/polyhedra/ http://www.uwgb.edu/dutchs/symmetry/symmetry.htm http://www.georgehart.com/virtual-polyhedra/vp.html http://en.wikipedia.org/wiki/Polygon http://en.wikipedia.org/wiki/Polyhedron