6-1C Exploring Polyhedrons

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6-1C Exploring Polyhedrons

• What is a polyhedron?
• What are the names of some polyhedrons that you
  are familiar with?
• How are polyhedrons classified?
• What is the relationship among polyhedron faces,
  edges and vertices?

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Definition

• A polyhedron is a solid whose faces are polygons.
• Faces are named in the same way as polygons.
• What are some polyhedrons that your are familiar
  with?
• Cubes, pyramids, and rectangular solids
• Look at the figure on page 410 in your book.
• Name a pentagonal face.

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Try It Page 410

• Polygons are classified by the number of sides
  they have.
• Polyhedrons are classified by the number of faces
  they have.
• See page 410

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Face Facts p. 411
Faces (F) Vertices (V) Edges (E)





4
4
6
a. b. c. d. e.
8
12
6
6
12
8
7
15
10
5
9
6
Is there a relationship among the faces, vertices
edges?
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Eulers Formula

• For any polyhedron, the relationship among the
  number of faces (F), vertices (V), and edges (E)
  is
• F V - E 2

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Leonhard Euler

• Lived 1707-1783
• Swiss mathematician
• Proved the formula showing the relationship among
  the faces, vertices and edges of polyhedron.

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• What is a polyhedron?
• A polyhedron is a solid whose faces are polygons.
• What are the names of some polyhedrons that you
  are familiar with?
• Cubes, pyramids, and rectangular solids.
• How are polyhedrons classified?
• Polyhedrons are classified by the number of faces
  they have.
• What is the relationship among polyhedron faces,
  edges and vertices?
• F V - E 2

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Assignment 6-1C

• Page 412, 1-8, 11-13, 16-18