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12.1 Exploring Solids

12.1 Exploring Solids

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12.1 Exploring Solids

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  1. 12.1 Exploring Solids Polyhedron Platonic Solids Cross Section

  2. Definition of a Polyhedron A polyhedron is a solid formed by many plane faces.

  3. Convex Polyhedron Convex Polyhedron are polyhedrons where any two points can be connected by a line segment

  4. Faces, Edges and Vertices A Cube has 6 Faces, 12 Edges and 8 Vertices.

  5. Cross section The cutting of a polyhedron or cone by a plane giving different shapes.

  6. Regular Polyhedron A regular polyhedron has regular polygons for faces

  7. Platonic Solids are regular polyhedrons

  8. Can you think of any use of a Icosahedrons?

  9. Euler’s Theorem The number of faces + number of vertices equals the number of edges plus 2. Icosahedrons has 20 faces, 12 vertices. How many Edges?

  10. Euler’s Theorem The number of faces + number of vertices equals the number of edges plus 2. Icosahedrons has 20 faces, 12 vertices. How many Edges?

  11. How many Edges on this shape? Edge = ½(Shape edges times Number of Shapes + Shape edges times Number of Shapes…..)

  12. How many Edges on this shape? Edge = ½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)

  13. How many Edges on this shape? Edge = 68 ½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)

  14. How many Vertices on this shape? Edge = 68, Faces = (6 +10 + 8) = 24

  15. How many Vertices on this shape? Edge = 68, Faces = (6 +10 + 8) = 24 24 + V = 68 + 2 24 + V = 70 V = 46

  16. Homework Page 723 – 726 # 10 – 30 even, 32 – 35 , 42- 52, 54, 55