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.

Supplies

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

Step 1: Building the Kaledoscope

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

Fit the 3 mirrors inside the box and mark that space.
Glue the mirrors to the box, in this case the mirrors I bought already came with stickers
All glued together? Then it's time to cut the calendars to size, removing the excess cardboard.

Step 2: Build One Part of Polyhedra - Cube

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

Step 3: Build One Part of Polyhedra - Rectangular Triangle

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

Step 4: Build One Part of Polyhedra - Equilateral Triangle

Draw 4 rectangular equilateral triangle and glue them together.

Step 5: Different Approaches in the Classroom

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.