12 1 solid figures lesson

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12 1 solid figures lesson

  1. 1. 12.1-12.5 Exploring SolidsNCSCOS: 2.04
  2. 2. New York Planetarium
  3. 3. Epcot Center
  4. 4. Defns. for 3-dimensional figuresDefns. for 3-dimensional figures• Polyhedron – a solid bounded by polygonsthat enclose a single region of shape. (nocurved parts & no openings!)• Faces – the polygons (or flat surfaces)• Edges – segments formed by theintersection of 2 faces• Vertex – point where three or more edgesintersect
  5. 5. Faces, Edges and VerticesThree dimensional (3D) shapes are defined by the number of faces,edges and vertices (corners) that they have.VERTEX(plural is vertices)EDGETETRAHEDRONFACE
  6. 6. ExEx: Is the figure a polyhedron? If so, howmany faces, edges, & vertices are there?Yes,F =V =E =569No, thereare curvedparts!Yes,F =V =E =7712
  7. 7. Types of Solids• Prism – 2 ≅ faces (called bases) in planes. i.e. first example• Pyramid – has 1 base, all other edgesconnect at the same vertex. i.e. lastexample• Cone – like a pyramid, but base is a circle.• Cylinder – 2  circle bases.or• Sphere – like a ball.
  8. 8. More definitions• Regular polyhedron – all faces are ≅,regular polygons. i.e. a cube• Convex polyhedron – all the polyhedrawe’ve seen so far are convex.• Concave polyhedron –“caves in”• Cross section – the intersection of a planeslicing through a solid. Good picture onp.720
  9. 9. 5 regular polyhedra• Also called platonic solids.• Turn to page 721 for good pictures at the topof the page.• Tetrahedron – 4 equilateral Δ faces• Cube (hexahedron) – 6 square faces• Octahedron – 8 equilateral Δ faces• Dodecahedron – 12 pentagon faces• Icosahedron – 20 equilateral Δ faces
  10. 10. ExEx: How many faces, edges, & vertices arethere?F =V =E =569F =V =E =7712F + V = E + 25 + 6 = 9 + 211 = 11F + V = E + 214 = 14

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