© Museum of the History of Science, Oxford

This instrument is actually a special type of sundials called a 'polyhedral dial' because it is made in a complicated shape. It can be used to tell the time in a number of different ways from the position of the sun. It is a very precious object and is completely covered in gold.
This particular sundial is very famous because it was made for Cardinal Wolsey. Cardinal Wolsey was one of Henry VIII's archbishops before Henry divorced his first wife, Catherine of Aragon, and was excommunicated from the Catholic Church, following which the Church of England became Protestant. We know it was made for Cardinal Wolsey because it has his coat of arms engraved on it as well as two pictures of a cardinal's hat.
This sundial is supposed to have been made for Cardinal Wolsey by a German craftsman called Nicholas Kratzer in about 1533. Nicholas Kratzer was employed by Henry VIII as his maker of sundials and clocks. Kratzer made many sundials and clocks for Henry VIII because at that time mathematical objects like sundials were very highly sought after. People who owned mathematical instruments used them to show that they were learned and cultured. This means that they wanted to show that they understood the new mathematical theories of the time and that they appreciated beautiful and complicated things.
Nicholas Kratzer was very friendly with another German craftsman who worked for Henry VIII. This was the famous artist Hans Holbein. Holbein painted many famous pictures of Henry VIII and people who visited Henry in his palace. Hans Holbein also painted a picture of his friend Nicholas Kratzer holding a sundial and surrounded by the tools he used to make mathematical instruments. It is in the Louvre Museum in Paris. Another painting by Holbein that has lots of mathematical objects in it is the Ambassadors. This is in the National Gallery in London. The mathematical instruments that Holbein painted in the Ambassadors painting are all very complicated and it is almost certain that Kratzer helped him to work out what they should look like.
In the Renaissance, 'polyhedral' dials like this one were like Formula 1 racing cars are now. They were less useful as things to be used everyday and more like things that had all the uptodate technology and theories built into them. They were made so that mathematicians and instrument makers could show off their skills and demonstrate that they had mastered all the new mathematical theories and techniques in something that actually worked.