Soccer balls and the Forbidden City

The Family and I visited the Forbidden City on a hot day of May last year. We’d not really anticipated how hot Beijing can get, and this day was a special scorcher.Guardian lion in the forbidden city We passed the three main audience halls in the central courtyard and turned into the section called the Palace of Tranquil Longevity, looking for the famous nine-dragon screen in front of the quarters of the famous Qianlong emperor. The sun was almost directly overhead. We had run out of water to drink. After admiring the dragons, we started looking for one of the food stalls inside the palace grounds. As a result, we did not pay too much attention to this guardian lion in front of the Qianlong emperor’s palace.

I was drawn back to my photo of this Tongshi, as bronze guardian lions are called in Mandarin, by an interesting article which connects it with Platonic solids, the design of footballs, and certain chemicals called buckyballs or fullerenes. A football is made by stitching together panels which are either pentagons or hexagons. Regular solids of this kind are called buckyballs. In the picture of one hemisphere of a football you see 6 pentagons. Since a football is symmetric, the half that you can’t see will have another 6 pentagons. A footballIt seems that mathematicians can prove that there must be exactly 12 pentagons on any structure that looks like a buckyball: and that the standard issue football is one such. The football, these new molecules, and Platonic solids like the dodecahedron are all tied together by these 12 pentagons. From the article I learned that the shape of the modern football was anticipated in the year 300 CE by a man named Pappus who lived in Alexandria. This figure was later discussed in a book published in 1509. The book was written by Luca Paccioli and illustrated by Leonardo da Vinci. In China such solids were first discussed much later, probably for the first time by Wending Mei in 1692.

The lion was made during the Qianlong emperor’s reign, so sometime between the years 1740 CE and 1800 CE. However, when you look carefully at the details, in the featured photo, of the ball held by the lion, you notice that it is not a buckyball. I can see only one pentagon. The article has photos of the bottom of the ball, and counts a few more, but nowhere like the 12 needed to make a buckyball. So it seems that the artist who made this deformed the shape of the ball quite significantly but could not dispense with pentagons. Still I like the fact that this shape brings together Plato, Leonardo da Vinci, and the Qianlong emperor.