Exploring Solids

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Section 12-1

• Exploring Solids

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Polyhedron

• Three dimensional closed figure formed by joining
  three or more polygons at their side.
• Plural polyhedra

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Parts of a Polyhedron
4

• Face Each polygon of the polyhedron
• Edge A line segment along which two faces meet
• Vertex A point where three or more edges meet

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Regular polyhedron

• Has faces that are congruent regular polygons

Example
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Convex Polyhedron

• If any two points on its surface can be connected
  by a segment that lies entirely inside or outside
  the polyhedron

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Concave Polyhedron

• If the segment goes outside the polyhedron

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Cross Section

• Intersection of a plane and a solid

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A plane and a solids intersection forms
different shapes.
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Examples of a Plane and a Cubes Cross Sections
Square
Trapezoid
Triangle
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Example of a Plane and a Spheres Cross Section
Circle
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Eulers Theorem

• The number of faces (F), vertices (V), and edges
  (E) of a polyhedron are related by the formula

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Platonic Solids

• Five regular polyhedra

• Tetrahedron 4 faces
• Cube 6 faces
• Octahedron 8 faces
• Dodecahedron 12 faces
• Icosahedron 20 faces

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Regular Tetrahedron
4
6
4
____ faces, ____ vertices, ____ edges
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Cube
8
12
6
____ faces, ____ vertices, ____ edges
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Regular Octahedron
6
12
8
____ faces, ____ vertices, ____ edges
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Regular Dodecahedron
20
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Regular Icosahedron
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