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 LESSON 3.  Euler’s Formula for Polygons (Lab) MATERIALS PROCEDURE:  Make the given shape and then record the number of faces, the number of points (vertex), and the total measure of face angles in the data chart below.  M = the total measure of all the face angles; v = the number of vertex points  To find the face angles, use the angle ruler.  Remember a square face would have 4 ninety degree angles for a total of 360.  A cube has 6 faces, so there would be a total of 6 x 360 for “Total measure of face angles.”
 Name Shapes needed # of faces # faces at vertex Total measure of face angles Tetrahedron 4 eq. triangles Hexahedron (cube) 6 squares Octahedron 8 eq. triangles
 Now look at the data that you have collected can you see a pattern that might help you get the information without really measuring.  (clue: has to do with multiples of 360)
 Icosahedron 20 triangles Dodecahedron 12 pentagons Hexagonal prism 6 squares   2 hexagons Cuboctahedron 8 eq. triangles 6 squares Truncated tetrahedron 4 hexagons 4 eq. triangles Rectangular prism 2 squares 4 rectangles Rhombohedron 2 squares 2 rectangles 4 isosceles triangles Prismatic Hexagonal dipyramid 12 isosceles triangles 6 rectangles
 Look at the data and see if you can make a formula that would work on all polygons.   Does this formula work for a cone or a cylinder?  Why or why not?
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