1. Nets and Categorising 3D Shapes
Slideshow 45, Mathematics
Mr Richard Sasaki

2. Objectives Understand how nets are built
Be able to build nets for various shapes using scissors and glue
Be able to categorise shapes using a Venn Diagram

3. Nets
What is a net?
A net is an unfolded 3D shape laid flat. Nets are usually made for polyhedra.
A net also makes it easy for us to see how many faces a shape has. Stating how many edges or vertices might be harder though.

4. Net - Cube
There are many ways to unfold the cube (or any 3D shape) but the most common is…
If this is rotated or flipped, it is still the same net. How many nets for the cube are there?

5. There are 11 nets for the cube!
Why can’t we physically build nets with these?
Answers
There are 11 nets for the cube!

6. If we make a net, we need flaps to glue, like this…
Note: Have a think about the properties of the shapes you are constructing!
Making Nets
If we make a net, we need flaps to glue, like this… × o
We don’t usually need to draw these though. o × × o
What edge will the flap marked touch?
We’ll look at this in more detail later.

7. We can use a Venn Diagram to categorise 3D shapes.
Categorising 3D Shapes
We can use a Venn Diagram to categorise 3D shapes.
Do you know what a Venn Diagram is?
Good!
Some categories could be…
Polyhedra -
Straight edges, flat faces
Regular Polyhedra -
Congruent polygon faces
Prisms -
Two, parallel, congruent bases
Antiprisms -
Twisted, connected by triangles
Pyramids -
Polyhedra with one base
Make a Venn diagram using these and more!

8. Categorising 3D Shapes Any other categories? 3D Shapes Polyhedra
Pyramids
Regular Polyhedra
Prisms
Antiprisms
Place the shapes you have made onto your Venn Diagram!

9. Categorising 3D Shapes 3D Shapes Icosidodecahedron
Small Stellated Dodecahedron
Dodecahedron
Pentagrammic Prism
Square-based Pyramid
Icosahedron
Octahedron
Hexagonal Antiprism
Snub Cube
Hexagonal Pyramid
Cylinder
Heptagonal Pyramid
Asymmetrical Cone
Square Antiprism
Tapered Cylinder
Pentagonal Prism
Truncated Tetrahedron
Octagonal Prism
Stellated Octahedron
Tetrahedron
Heptagonal Antiprism
Cone
Triangular Prism
Pentagonal Pyramid
Octagonal Antiprism
Cube
Polyhedra
Regular Polyhedra
Prisms
Pyramids
Antiprisms

10. Answers - Easy Tetrahedron Cuboid Cylinder Cylinder Cuboid Cuboid

11. Hexagonal Based Pyramid
Answers - Medium
Triangular Prism
Pentagonal Prism
Hexagonal Based Pyramid
Octagonal Prism
Pentagonal Prism
Hexagonal Based Pyramid
Octagonal Prism
Each circular face is connected to another by a point (a point has zero size).

12. Answers - Hard 5 2 2 5 3 4 Octahedron 3 4 1 1 8 faces, 6 vertices
6−𝐸+8=2⇒𝐸=12⇒12 Edges
Two faces will overlap (the two at the top).
You need to look at the relationships between various prisms.
𝑉=2𝐹−4