Octant Kaleidoscope

This project shows once again how simple and beautiful mathematics can be. In a cheap and quick way we can better understand the world of polyhedra.

Kaleidoscope is an optical instrument used to create symmetrical visual effects with the aid of a set of mirrors.

Why octant? Octant comes from eight, that is, this kaleidoscope allows us to see some polyhedra by placing only one of its parts, it reproduces the other seven.

• Cardboard - You can use cardboard boxes that I'm sure we all have at home.

• 3x Mirrors - Can be purchased in any supermarket

• Scissors and box cutters

• Ruler and pencil

• Glue and tape

You can use a box to support the walls of the kaledoscope.

1. Fit the 3 mirrors inside the box and mark that space.

2. Glue the mirrors to the box, in this case the mirrors I bought already came with stickers

3. All glued together? Then it's time to cut the calendars to size, removing the excess cardboard.

Building a cube is the simplest and most intuitive. Draw six squares measuring 6x6cm on cardboard. Cut and glue them together. Done!

Draw 3 rectangular triangles and glue them together, using the shape created to create the other missing face.

Draw 4 rectangular equilateral triangle and glue them together.

Depending on the teaching level we can do a more guided activity or appeal to the creativity and ingenuity of the students.

For a more guided activity we can follow the steps of this project for students to create the solids and then see the final result.

If we want a more exploratory approach we can give the final polyhedra to the students and challenge them to think which basic unit forms one of the eight parts of the polyhedron.

If the school already has 3D printers, more durable models can be made and the concepts of 3D modelling can also be explored.

Also a pdf with the summary of the different triangles.