Maksym Khomyshyn 3.C

Definition, characteristics and classification

Triangle Square Pentagon

 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

Isn‘t a polygon Is a polygon

6 vertexes 6 edges 1 body

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

α<180° α>180° ConvexConcave

Definition and characteristics

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

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

Face Edge Vertex Body

 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

Nature polyhedra around us

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

In chemistry Carbon nanotubes Metal nanoparticles Crystals

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

Resources: Eric W. Weisstein - Polyhedron George W. Hart - Polyhedra from Symmetric Placement of Regular Polygons