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.