Types of 3-D Objects

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.

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