So abstract and foreign to our eyes that we let it escape our attention while we talk about all our theoretical points of view and divergences from what is symmetrical?
In the past, new scientific discoveries, strange finds, and striking pieces of original artwork were greeted with awe and wonder. It became popular during the Renaissance to build a "cabinet of curiosities" to display a private collection of art and natural objects of which the owner was extremely proud. These groups of objects were at first housed in an actual cabinet or ornate piece of furniture, known as Wunderkammern or Wunderkabinetts. They are simultaneously pieces of furniture and the collections of items within them.
In the exhibits of these early Wunderkammern, owners might display strange, beautiful, mysterious, and precious marvels like starfish, monkey teeth, alligator skins, phosphorescent minerals, Indian canoes, Egyptian figurines, and “unicorn tails.” Rich art patrons would display their new art acquisitions in the intimate backdrop of a prized spot in an ornate carved cabinet. At Kensington castle, Sir Walter Cope is said to have displayed, “holy relics from a Spanish ship; earthen pitchers and porcelain from China; a Madonna made of feathers; a back-scratcher; a Javanese costume, Arabian coats; the horn and tail of a rhinoceros; the baubles and bells of Henry VIII's fool; and a Turkish emperor's golden seal.” The collections demonstrated manmade wonders and the diversity of God’s creations as well as a fascination with new scientific approaches to the study of natural phenomena. Each collection’s commitment to miscellany dependended on the idiosyncratic interests of the collector.
So it was again important to bring people back to the ways of geometry working in spaces, that although seemingly detached from our reality is the underlying basis of the physics involved.
Mine is a layman's perspective so I cannot say for certain that all I write here will be of value. It is up to you whether you think it important or not.
Figure 2. Clebsch's Diagonal Surface: Wonderful.
Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.
The Museum when thought in context of "Platonic solids" was some what of a contention when I showed it's location in early historical context as a artifact.
Shown here are the models in the mathematical wunderkammer located in the Department of Mathematics at the University of Arizona. Like those in most modern mathematics departments, the collection is a combination of locally-made student and faculty projects together with a variety of commercially produced models. Sadly, a century since their Golden Age, many of the models are in disrepair and much of their documentation has been lost. However, some recent detective work, with the help of the Smithsonian Institution in Washington, has helped the department identify models by the American educators W. W. Ross and R. P. Baker in the collection.
Also see here for further thoughts on this
I thought it important to quickly post this so that people understand that "a glass case" can hold many things for inspection, but in this case ,I was referring to the geometrical forms. If any of these form were to show symmetry in action which of these would do so? Sylvestor surfaces?
An attempt in Latex to map these functions from a layman's perspective. What use if I cannot understand the mathematical language as it is written, yet, I can see "acrobatically" the way geometry works in space?