From Wikipedia: https://en.wikipedia.org/wiki/Ivory_carving
"By the 18th century China had a considerable market in items such as figures made for export to Europe, and from the Meiji Period Japan followed. Japanese ivory for the domestic market had traditionally mostly been small objects such as netsuke, for which ivory was used from the 17th century, or little inlays for sword-fittings and the like, but in the later 19th century, using African ivory, pieces became as large as the material would allow, and carved with virtuosic skill. A speciality was round puzzle balls of openwork that contained a series of smaller balls, freely rotating, inside them, a tribute to the patience of Asian craftsmen."
Usually, many of these balls have a decorated stand made of ivory too.
Chinese puzzle ball, with openwork and a series of twelve smaller balls, ivory, 19th century. British Museum. Original photograph from Ged Carroll
"Originally, they (Chinese puzzle balls) were made almost exclusively from ivory, or the tusks of elephants and were the playthings of rich men because of the time and effort involved in making them. ... Usually, puzzle balls are symbols of good luck, and are decorated with a variety of feng shui symbols. The outermost layer often features the phoenix and dragon, symbols of yin and yang. The phoenix represents the wife while the dragon is the husband and emperor, and balls decorated with these symbols are thought to bring good luck and happiness to a marriage. In fact, almost all of the symbols most commonly associated with puzzle balls are associated with ensuring a long and happy marriage. Some balls even have different symbols on different layers, though the most common is a highly decorative outer ball and ‘latticed’ balls inside (with geometric patterns of holes)."
Detail of an ivory ball on show in the German Rautenstrauch-Joest Museum. It has 16 layers, which can spin. Courtesy Till Niermann , Wikipedia.
In the above image we see an example of Canton ivory carving. From Wikipedia (on the Lingnan culture or Cantonese culture). "Canton ivory woodcarving is another well-known product from Lingnan. With a history of 2000 years, it traditionally uses ivory as raw material to make sculptures, with the Canton-style renowned for being particularly delicate and detailed without being brittle. The Cantonese people have also successfully produced the legendary craft product - Ivory ball. After the 1980s, however, international ivory trade has been banned. This results in the Cantonese people now trying to find substitute materials - materials that look and feel like but are actually not ivory - in their attempt to pass on this ancient art."
"Chinese puzzle balls are ornate decorative items that consist of several concentric spheres, each of which rotates freely, carved from the same piece of material. ... These detailed works of art are usually made up of at least 3 to 7 layers, but the world’s largest puzzle ball is actually made of 42 concentric balls all enclosed one within the other. Although the inner balls can be manipulated to align all the holes, Chinese puzzle balls got their name from people who, through the ages, pondered the mystery of making such objects. So how exactly are puzzle balls made? .... Chinese masters rotate a solid ball on a lathe and start by drilling holes toward the center of the objects. Then, using special “L”-shaped tools, they begin to separate the innermost balls. ... Because it is easier to work with, the exterior shell is the most elaborately carved, usually featuring an intertwined dragon and a phoenix."
Antikitera.net tells us that the first puzzle balls appeared during the Song Dynasty, around 1000 d.C.
After having shown the Chinese ivory balls, it seems that the puzzle balls became popular in Europe thanks to Chinese products of the later XIXth century. However, puzzle balls existed in Europe in XVI or XVII century. Here an example.
European puzzle ball, XVI-XVII Century (Image Courtesy: Maureen and Renato Bucci, Italy). It was exhibited with a rosary having the beads made in the same manner of the ball.
The rosary, XVI-XVII Century (Image Courtesy: Maureen and Renato Bucci, Italy).
The ball shown in the image is remarkable because it looks like a Roman Dodecahedron. Actually Renato Bucci was so kind to send me the picture because of this similarity. Probably, this was an object of a Wunderkammer (in italiano, camera delle meraviglie o gabinetto delle curiosità o delle meraviglie), encyclopedic collections of objects of the Reinassance Europe.
"The Kunstkammer was regarded as a microcosm or theater of the world, and a memory theater. The Kunstkammer conveyed symbolically the patron's control of the world through its indoor, microscopic reproduction."
Here an example of Kunstkammer
Let me conclude remarking that today puzzle balls are created too. Here the image of one of them, which is showing "puzzle dodecahedra". The artist that created it is Pierre Meyer is an artist who works with ivory. https://www.maitresdart.com/pierre_meyer-40/parcours_et_realisations.html
Pierre Meyer's ivory "puzzle dodecahedron".
Also "new production of ornamental turning ivory of '600" is evidenced by the works of Andrea Pacciani, architect in Parma, by the web https://www.etsy.com/it/listing/225172225/tornitura-ornamentale-da-un-modello-in. A piece "is inspired by a piece of the museum's collection of Rosenborg in Denmark (*). Another piece is inspiered to the drawings of Grollier de Serviere, (1596–1689), French inventor and ornamental turner. According to Andrea, "Thanks to the new generation of 3D technologies we could bring back the light of contemporary production about this object collection of great visual impact". That is, new technologies for creating objecs for our modern Wunderkammer.
(*) the reader can see the pieces at http://www.bobkatsjaunt.com/denmark.html.
A drawing from a book on the works of Grollier de Serviere