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Geometry: Part 2

Geometry: Part 2. 3-D figures. Polyhedron. 3-dimensional analog of a polygon Closed surface made up of polygons Any 2 polygons may have only one shared edge. Vertex. Edge. Face. Prism. Polyhedron with 2 opposite faces that are identical polygons Faces are called bases

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Geometry: Part 2

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  1. Geometry: Part 2 3-D figures

  2. Polyhedron • 3-dimensional analog of a polygon • Closed surface made up of polygons • Any 2 polygons may have only one shared edge Vertex Edge Face

  3. Prism • Polyhedron with 2 opposite faces that are identical polygons • Faces are called bases • Bases are joined by lateral faces • If the lateral face is a rectangle it is a right prism

  4. 2 hexagons for bases Right Hexagonal prism 2 rectangles for bases Right rectangular prism Examples: base Lateral face

  5. Geometry in the Real World

  6. Pyramid • Base is any regular polygon • All sides are triangles

  7. Platonic Solids • All sides are equal • All angles are the same • All faces are identical • Same number of polygons meet at each vertex • Only five solids meet these criteria: Platonic solids

  8. Tetrahedron • Composed of 4 equilateral triangles • 3 triangles meet at vertex • Represented fire to the ancient Greeks

  9. Hexahedron (Cube) • Composed of 6 squares • 3 squares meet at a vertex • Represented the stable earth

  10. Octahedron • Composed of 8 equilateral triangles • 4 triangles meet at a vertex • Represented air

  11. Dodecahedron • Composed of 12 equilateral pentagons • 3 pentagons meet at a vertex • Represented the 12 signs of the Zodiac

  12. Icosahedron • Composed of 20 equilateral triangles • 5 triangles meet at a vertex • Represented water

  13. Models of Polyhedra

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