Divine and Destructive: The Truncated Icosahedron

Podcast – Professor Elliot's Bookshelf

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It is a shape found in a lot of places. Its influence can be found throughout history and has had an impact on millions, if not billions of humans. The truncated icosahedron has 32 sides; made up of 20 hexagons and 12 pentagons. The first known illustration of this shape was drawn by Leonardo da Vinci. In 1447, he included it in a book created with his close friend Luca Pacioli called De Divina Proportione: The Divine Proportion. Since then, the truncated icosahedron has been seen in a lot of places.

A truncated icosahedron next to an association football.
Photo by Aaron Rotenberg

The 1970 World Cup was to be televised across the globe. When Adidas was hired to create their first official ball, they decided to focus on two things: creating the roundest ball of all time and creating a ball that could be easily seen on black and white television sets. The Telstar ball was born. It is the most well known design for these balls; the shape of an overinflated truncated icosahedron. Why was it named Telstar? The 12 black pentagons and 20 white hexagons looked similar to the black and white pattern of the Telstar communications satellite.

The Telstar communications satellite

While experimenting with laser vaporized carbon, in 1985 a group from Rice University came across something interesting. The molecules in the vapor, according to their measurements, had a weight equal to 60 atoms each. The shape of this molecule, I’m sure you’d guess, was just like a soccer ball. Carbon₆₀ was the first new form of Carbon discovered in possibly a millennium. It was the first carbon form to dissolve in water and the first molecule to be able to trap an atom in its interior. This opened up vast new realms of scientific discovery for the element and led to a Nobel prize given to the group.

The structure of Buckminsterfullerene (a buckyball)

Perhaps the most notorious use of the shape is also the least seen… The Fat Man bomb, detonated over Nagasaki, owed it’s design to that shape. Shock waves from the detonators need to be focused onto the center of the weapon. 12 pentagonal and 20 hexagonal lenses line the edges of the bomb, making the truncated icosahedron possibly the most destructive shape in history.

The lenses are labelled #6 & #7.
Other items marked:
1. AN 219 destruct fuse
2. Archie radar antenna
3. Plate with batteries (to detonate charge surrounding nuclear components)
4. X-Unit, a firing set placed near the charge
5. Hinge fixing the two ellipsoidal parts of the bomb
8. California Parachute tail (aluminium)
9. Dural casing, ~140 cm inner diameter
10. Cones that contained the whole sphere
11. Explosive lenses (low and high velocity)
12. Nuclear material (see other figure for details about the different layers)
13. Plate with instruments (radars, baroswitches and timers)
14. Barotube collector

Music: Piano Concerto in A minor by Edvard Grieg, performed by the Skidmore College Orchestra