3.3 Developments (nets)

How to sketch Developments, commonly known as Nets, that include glue tabs and mechanical joining methods, required to form: 

Prisms Cones Cylinders Pyramids

In geometry, a Net is a 2-dimensional shape that can be folded to form a 3-dimensional object. Nets are useful for visualising and understanding the surface area of 3D shapes. 

Typically in industry Nets are created using the Die Cutting process. 

If you were to create and cut one in a school workshop you would use a safety ruler, cutting mat, scalpel / craft knife / cutting knife. The rulers and knife would be used to cut, score and fold the Net into the desired shape. Glue would be added to the Gluing tabs to join the Net together. Additionally, a clear plastic such as acrylic, acetate or thin polycarbonate sheet can be added for 'windows' to see the product or goods inside the package. 

Glue tabs for nets are small flaps or extensions on the edges of a 2D net that are used to connect the faces of a 3D shape together. They are typically coated with an adhesive so that when folded and pressed against the adjacent face, they create a secure bond. They always have a small angle at the end of the flap (with a very small round / fillet) so that they can fold (fit) inside other cardboad sides. A rectangular box will always have 6 sides! 

The button below takes you to a website that shows you how to start drawing out any 2D to 3D Net.

To sketch a net for a prism, start by drawing the base polygon, then draw rectangles (representing the lateral faces) connected to each side of the base polygon, ensuring the length of the rectangles corresponds to the height of the prism, and finally, draw a congruent base polygon on the opposite side of the rectangles, connecting them to complete the net; remember that the arrangement of the rectangles and bases can vary depending on the prism's orientation. 

Some Prism boxes are fairly simple to sketch, particularly the ones based on a traingle (Toblerone package) but complexity can be added with curves and mechanical joining (locking) methods. See the examples below. 

Note the Cut lines; the dashed lines for folding the glue tabs. You should see that the two circles (top and bottom) for the cylidner are connected by a very think piece of card which will be folded. 

There are a number of ways that you could sketch a net for a Pyramid/ The examples shown online often forget to show which are score (dashed) lines for folding and which are cut lines. The example on the right is an excellent example of creating a pyramid however all lines suggest they are cut lines and so it would fall to pieces. You must remember to use dashed lines. 

To note is that if the square for the bottom of the pyramid was 40mm x 40mm then the length of the triangle pieces would be 60mm. The square is usually 2/3rds of the length of the triangle (height of the pyramid)!