Three-Dimensional Figures

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Notes Three-Dimensional Figures Polyhedra (the plural of Polyhedron) are three dimensional versions of polygons. They are made up of polygons. They are solid (no holes) and closed. Polyhedra fall into two major classes: Pyramids and Prisms. Note: Prisms and Pyramids are always named “based” on their bases. A Prism with a square base is called a Square Prism; a pyramid with a square base is called a Square Pyramid; a prism with a base that’s an octagon is called an Octagonal Prism; and so on. General Classes of Polyhedra 1) Prism - polyhedron with two opposite faces identical to each other. These opposite faces are called bases. The other faces are called lateral faces. Using the Power Solids, find all of the Prisms. Decide which faces are the bases, and which faces are the lateral faces. Then write the name of each of the prisms that you found: 2) Pyramid - polyhedron with a top "point" (called an apex), where all lateral faces meet. Using the Power Solids, find the two Pyramids. Decide which face is the base, and which faces are the lateral faces. Write the names of those two pyramids below. Other Three Dimensional Figures 1) Cylinder - curved shape analogous to a prism, except with circles for bases. Question: If the two circles are bases, what is the lateral “face”? 2) Cone - curved shape analogous to a pyramid, except with a circle for a base. Question: If the circle is the base, what is the lateral "face"? Note: The bases of cones and cylinders do not have to be circles (they could be ovals, for example), but we will pay attention to only those with circular bases. 3) Sphere - three dimensional version of a circle - a sphere is the set of all points in three dimensional space that are the same distance from a fixed point in space. This fixed point is called the center of the sphere. Page 1 of 2 Notes Note: The line segment that joins the center of the sphere to a point on the sphere is called the radius; a line segment that joins two points on the sphere that intersects the center of the sphere is called the diameter. Euler's Formula: Let V stand for the number of Vertices, let E stand for the number of Edges, and let F stand for the number of Faces on a simple closed surface. Complete the table below using the Power Solids. Number of Number of Number of Shape: Name: faces edges vertices Look at the last three columns. What patterns do you see? Write those patterns below: Page 2 of 2 .

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