Stuffed Toys

Introduction

The Stuffed Toys is aDALESTapplication. This application is based on the idea of cube net (folding/unfolging dice). After spending some time thinking about what dice-net-based application is worth implementing it was decided that it must be:

**unique**, i.e. not done before (or at least not common)**meaningful**, i.e. to promote activities which are (almost) impossible to do easily in real life

For example, finding a net that can fold in a cube is something which can be done easily with a paper, and there are dozens of programs that visualize this activity. That's why it was concluded to implement the reversed process. And here come the Stuffed Toys application. The core idea is that the user has a stuffed cube. Some edges are unripped, so the cube can be unfolded into a planar structure. There are 11 topologically different cube-nets (without rotation and symmetry) and the goal is to identify which of them will become the stuffed cube after unfolding. When the cube is unripped, it remains relatively intact. The user can freely rotate it to inspect how faces are connected

After playing with Stuffed Toys literally hundreds of times, we do confirm that the reversed mapping problem is not easier than the original one. It also requires a significant 3D imagination, which can be developed with this application in a natural way. The Stuffed Toys have two sets of toys to explore. The first set is only of white cubes. The other one is with real-looking colored toys: normal ball, rugby ball, cube, egg, soft and hard pyramid, random irregularily-shaped pebbles, etc. All of them are composed of 6 faces which can be unfolded just like the cube. The only difference is that it is harder

Activities

- Examine a ripped cube and predict the shape of the net after unfolding
- Make a paper models of the 11 cube nets and fold (one of) them into the ripped cube shown on the screen
- Identify specific face connections which provide clues of the unfolded net; try to determine the conditions which indicate the possibility or impossibility of a specific net
- Make a competition of guessing 10 stuffed cubes in a row
- Solve the same problem but with stuffed toys
- Try to figure out what knowledge used in solving stuffed cubes can be applied to solving stuffed toys? Is a stuffed sphere identical to a stuffed toy?
- Name (describe) other toys which are composed of 6 faces connected in the same way as in the cube. Can they be solved in the same way?