The Qubits Building Set is capable of building impressive 3D spherical structures. When you study these structures you might wonder what polyhedra they relate to? We wondered ourselves what those polyhedra would look like so we made a polyhedra for each of the 7 major shapes that our toy is able to construct. This document allows you to build them yourself for free. Just print out the pages with the “GEOMETRICAL NETS”. The nets drepresent the 3D shape when it is folded flat. After printing on stiff paper, cut them out, fold them along all the lines and tape them together into a 3D shape with small pieces of tape in the inside. It is a craft called “Paper Polyhedra.”

In doing this exercise we quickly realized that the polyhedra formed were “GOLDEN POLYHEDRA”. That is to say, there are line lengths that are PHI – 1.618… included in the polyhedra. This is a terrific educational development because it allows us to introduce students of all ages to this fascinating aspect of Mathematics.

This number 1.618 was called the “GOLDEN RATIO” by the Ancient Greeks. The Golden Ratio is also known as the Golden Section. the Golden Mean or the Golden Rectangle. The Ancient Egyptians used the Golden Ratio to build the pyramids. In fact the Great Pyramids show the first example of using the Golden Ratio in Architecture. The Egyptians accomplished all this back in around 205 – 3100 BC.

In India the Golden Mean was used in the construction of the Taj Mahal which was completed in 1648. Leonardo da Vinci utilized the Golden Ratio intensively while creating inventions. He even included it in many of his paintings. He called it the Divine Proportion. The architect Le Corbusier applied the Golden Ratio specifically with his modular system which he saw as a continuation of the traditions found in the work of the renaissance architect Leon Battista Alberti.

PHI 1.618… is not to be confused with PI which is 3.14… The ratio of a circle’s circumference to its diameter. Both are important to mathematics and NATURE. Nautilus Shells are perhaps the most famous example of PHI geometric beauty. PHI is a number without a arithmetic solution, the digits simply continue for eternity without repeating themselves. PI is similar however it is an irrational number, just not an infinite number.

So sit down with a scissors and tape. The manipulative effect of working with small pieces of paper with improve the dexterity of nearly anyone. The result will be 7 of the coolest 3D shapes our toy can geometrically describe. Two of these shapes were already discovered by Archimedes back in 287-212 bc. The Cuboctahedron and Icosidodecahedron were two of the thirteen shapes he created. It is fun to realize that our toy made over two thousands years later is harkening back to this moment of discovery. It was a “Eureka Moment”.