I hope you enjoyed the introduction to 3-D objects and the discussion about “What is a 3-D Object?”

As previously discussed, 3-D objects fall into 4 primary categories: platonic solids, prism, antiprism, and pyramid.  Now we will discuss the types of 3-D objects in each of these categories.  This discussion will identify what shapes exist in each object and how many sides/”faces” each object contains.  The shapes I have chosen for our first explorations are: triangle, square/rectangle, pentagon, hexagon, octagon, and 5-sided star.

Using Platonic Solids

• Tetrahedron – contains all triangles and has 4 sides/”faces”
• Cube – contains all squares and has 6 sides/”faces”
• Octahedron – contains all triangles and has 8 sides/”faces”
• Dodecahedron – contains all pentagons and has 12 sides/”faces”
• Icosahedron – contains all triangles and has 20 sides/”faces”

Using Prisms (One rectangular side per “base shape” side)

• Triangular Prism
  • Top/bottom – triangle
  • 3 rectanglular sides
  • 5 total “faces”
• Square/rectangular Prism (same as Cube when squares used)
  • Top/bottom – square or rectangle
  • 4 rectangular or square sides
  • 6 total “faces”
• Pentagonal Prism
  • Top/bottom – pentagon
  • 5 rectangular sides
  • 7 total “faces”
• Hexagonal Prism
  • Top/bottom – hexagon
  • 6 rectangular sides
  • 8 total “faces”
• Octagonal Prism
  • Top/bottom – octagon
  • 8 rectangular sides
  • 10 total “faces”
• 5-sided Star Prism
  • Top/bottom – 5-sided star
  • 10 rectangular sides
  • 12 total “faces”

Using Antiprisms (Two triangular sides per “base shape” side)

• Triangular Antiprism (sames as Octahedron)
  • Top/Bottom – Triangle
  • 6 triangular sides
  • 8 total “faces”
• Square/rectangular Antiprism
  • Top/Bottom – Square/rectangle
  • 8 triangular sides
  • 10 total “faces”
• Pentagonal Antiprism
  • Top/Bottom – Pentagon
  • 10 triangular sides
  • 12 total “faces”
• Hexagonal Antiprism
  • Top/Bottom – Hexagon
  • 12 triangular sides
  • 14 total “faces”
• Octagonal Antiprism
  • Top/Bottom – Octagon
  • 16 triangular sides
  • 18 total “faces”
• 5-sided Star Antiprism
  • Top/Bottom – 5-sided Star
  • 10 triangular sides
  • 12 total “faces”

Using Pyramids (One triangular side per “base shape” side)

• Triangular Pyramid
  • Base – Triangle
  • 3 triangular sides
  • 4 total “faces”
• Square/rectangular Pyramid
  • Base – Square
  • 4 triangular sides
  • 5 total “faces”
• Pentagonal Pyramid
  • Base – Pentagon
  • 5 triangular sides
  • 6 total “faces”
• Hexagonal Pyramid
  • Base – Hexagon
  • 6 triangular sides
  • 7 total “faces”
• Octagonal Pyramid
  • Base – Octagon
  • 8 triangular sides
  • 9 total “faces”
• 5-sided Star Pyramid
  • Base – Star
  • 10 triangular sides
  • 11 total “faces”

What other shapes would you like to see explored?  Please let us know.