08/01/2019

Craftsmanship anticipated the discovery of polyhedra.

Reprodução/Giramundos

Brazilian culture is so rich that some things often go unnoticed even by the most attentive eyes. Traditional in the country's interior, the handcrafted ornaments known as "giramundos" are an incredible embodiment of an interesting polyhedron: the rhombic hexecontahedron. Cri, cri, cri…
Didn't understand anything? The explanation is simple: rhombic hexecontahedrons are solids composed of 60 rhombuses that, when joined together, form a kind of star. Not surprisingly, in Brazilian tradition, handicrafts made from this polyhedron are also commonly called "stars of happiness." But we only made this connection after reading a very interesting post on the subject on the blog of British scientist Stephen Wolfram .

The rhombic hexecontahedron was discovered in 1940 by the German mathematician Helmut Unkelbach, but the tradition of making the "giramundo" (a type of inflatable toy) in Brazil is much older. According to artisans, giramundos have been produced—using cardboard and fabric—for over 200 years. The art of assembling them has been passed down from mothers to daughters through oral tradition.
The few accounts of its origin explain that in some regions of Brazil it was common for mothers to sew a "giramundo" (a type of small, round, round, and round) as a gift for their daughter before marriage. One side was left open so that she could put money inside for her daughter's use in case of an emergency. They were usually "disguised" as a pincushion, kept among sewing supplies, so that the sons-in-law wouldn't spend the money.
In other parts of the country, the giramundo was used as a kind of amulet. Hung on the doors of houses, their function was to decorate and bring good luck as they spun in the wind.

Names and clues to their origin

Cultural diversity has led to giramundos acquiring different names in different regions of Brazil, with diverse meanings. It is common to call them mandacaru flower, carambola, star, secret, piggy bank, star of happiness, star of Saint James, star of Saint Michael, thorn bush, needle bush, and Pindaíva (or Pindaíba).
For example, in the southern border region of the country, it was known as the Star of Saint Michael and produced by healers (or witches, as you prefer), who sewed prayers into it to bring health to someone. Meanwhile, in the interior of São Paulo state, young women made the little boxes to use as jewelry boxes.
In the mountainous region of Rio de Janeiro, the "giramundos" (a type of flower crown) were a kind of rite of passage. On their wedding day, mothers would gift their daughters with a star made from scraps of fabric from the young woman's entire life—baptism, birthdays, and other important dates. The star symbolized part of the young woman's history, which she would carry as a memento, as she was beginning a new chapter as a mother. It is believed that the "giramundos" arrived in Brazil with Portuguese girls who came with the Royal Family in the first half of the 19th century. Initially, it was a tradition of wealthy Portuguese families, whose daughters married sugar and coffee farmers in rural areas. The "giramundos" spread until they became common among the poor. With the advent of urbanization, the tradition was lost. What is certain is that until the 1950s, rural schools in the south of the country still taught the art of making "giramundos" to girls.

Now, Mathematics
The name hexecontahedron comes from the Greek word hexeconta, which means 60. Not surprisingly, the polyhedron has 60 faces. But the piece's "surname"—rhombic—is what distinguishes it. It means that it is formed by golden rhombuses that are in the golden ratio.
There is a slight difference between the geometric solid and the "giramundo" (a Brazilian term for a circular object), namely the angle of the rhombuses. While in Brazilian crafts each rhombus has a 60º angle, in mathematics it has exactly 63º, and only with this measurement can it fit together perfectly. These are details that don't change the fact that, unintentionally, Brazilian culture "created" a polyhedron without knowing it was doing mathematics with its hands. Want to delve deeper into the subject? Check out Wolfram's material .