Look at page 193 in your explorations book. Ignore the letters--they are not used for this. Each figure is made up of 5 squares that may or may not be able to form 5 sides of a cube. We call this a net. Which of the 12 nets will form a cube?

Agenda Go over warm up. Discuss Exams Complete discussion of 2-Dimensional Geometry Polyhedra attributes Exploration 8.15 and 8.17 Examining the Regular Polyhedra 3 Dimensions require 3 views Assign Homework

Polyhedra On your tables, you will find sets of polyhedra. Examine them. Compare and contrast polyhedra and polygons. What is true about all prisms? What is true about all pyramids? What is true about prisms and pyramids, but not about other polyhedra?

Attributes In a polygon, we call it a side. In a polyhedron, we call it a(n) __________. In a polygon, we call it a vertex. In a polyhedron, we call it a(n) __________. In a polygon, there is one plane interior, and so we do not name it. In a polyhedron, there are many plane interiors, and we call them __________.

Exploration 8.15 Do Part 1 #1 and 2 for figures a - d and g. Create the 5 regular polyhedra--cut out the nets and tape the sides together. Then, mark or color the vertices, edges, and faces. Record their numbers as well. Can you identify a relationship between the faces, edges, and vertices of all these polyhedra?

Exploration 8.15 follow-up ID=70http://illuminations.nctm.org/ActivityDetail.aspx? ID=70 The relationship you found is called Euler’s formula, or Euler’s Law. It works for any polyhedron. Vertices + Faces = Edges + 2 It does not work for solids like cylinders or cones. Can you explain why not?

Constructing and Deconstructing Solids A solid is formed by a 3-dimensional figure and its interior. Because a solid has 3 dimensions, it is easy to miss hidden aspects when viewed from only one perspective. Hence, we typically draw using 3 views: front, side, and top.

Let’s do one together. FrontSideTop

Exploration 8.17 In class, we will do Part 4 #1a - f. –I will show you how to describe your answer. At home, you will do Part 4 #2a - f. –I will show you how to write your answer.