Regular Polygons:

You can tile a floor with triangles squares or hexagons….

Angle of a regular k-gon = 108(k-2)/k degrees K=3 gives 60 degrees But not with pentagons! Angle of a regular k-gon = 108(k-2)/k degrees K=3 gives 60 degrees K=4 gives 90 degrees K=5 gives 108 degrees, etc….. k Angle Measure 360/Angle Measure 3 60 6 4 90 5 108 3.333333333 120 7 128.5714286 2.8 8 135 2.666666667 9 140 2.571428571 10 144 2.5

Now let’s move to 3 dimensions Put regular polygons together to form regular polyhedral…. Can we always do this?