6-3B Regular Polyhedrons

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6-3B Regular Polyhedrons

• What is a regular polyhedron?
• What are Platonic solids?
• What are the names of the Platonic solids?

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Regular Polyhedron

• Congruent edges and faces
• Faces that are regular polygons
• An equal number of edges meeting at each vertex
• A convex regular polyhedron is one with no
  dents.

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Platonic Solids

• Platonic Solids are five convex regular
  polyhedrons discovered over 2,000 years ago and
  named in honor of the Greek philosopher Plato.
  They are
• Regular tetrahedron
• Regular hexahedron
• Regular octahedron
• Regular dodecahedron
• Regular icosahedron

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Regular tetrahedron
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Regular hexahedron
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Regular octahedron
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Regular dodecahedron
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Regular icosahedron
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Purely Platonic
Name Type of face of faces of vertices of edges
Tetrahedron Triangle 4 6 4
Hexahedron Square 6 12 8
Octahedron Triangle 8 12 6
Dodecahedron Pentagon 12 20 30
Isosahedron Triangle 20 12 30
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Name the convex regular polyhedron that has the
given set of characteristics

• Five equilateral triangular faces meet at each
  vertex
• Square faces
• Three equilateral triangular faces meet at each
  vertex

• Regular icosahedron
• Regular hexahedron
• Regular tetrahedron

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Do platonic solids occur in nature?

• Chrome alum octahedrons
• Salt hexahedrons
• Sugar

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Concave regular polyhedrons
Great Icosahedron
Great Stellated Dodecahedron
Small Stellated Dodecahedron
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• What is a regular polyhedron?
• Congruent edges and faces, faces that are regular
  polygons, and an equal number of edges meeting at
  each vertex.
• What are Platonic solids?
• Platonic Solids are five convex regular
  polyhedrons.
• What are the names of the Platonic solids?
• Tetrahedron, hexahedron, octahedron,
  dodecahedron, icosahedron.

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Assignment 6-3B

• Page 450,
• 1-10,23-24