Although it certainly won't be obvious if you go searching the net, Ibico does not exist! There are hundreds if not thousands of listings for Ibico products and supplies: how can this be? One possibility is that the web page is out of date, but that can't possibly account for all of them.
Ibico AG, with headquarters in Switzerland, for years built binding and laminating machines and established a very good reputation. At least six patents were registered by the company, one dated 1986. In 1998 the company was bought out by General Binding Corporation (GBC). However, the new owner took advantage of the brand name and maintained the Ibico machines as well as its own products. This continued until 2005, when the Ibico manufacturer's name was dropped; but it was retained as a model name. (That's why you'll almost always find GBC and Ibico products mentioned in the same breath).
Many hundreds of Ibico products were dropped; many, as noted, retained the model name; and a great many were simply renamed. A number of the laminating products named "Ibi..." (such as the Ibimatic) were renamed "Combind xxx". Similarly although not as consistently, Ibico's desktop binding products were renamed GBC something-or-other, as were the punching products. To find out if any particular Ibico product still exists, reincarnated or not, asking those in the know or doing web searches will find the answer.
Ibico AG still exists, with an address in Zurich, Switzerland. It is associated with the "Poly..." binding and duplicating machines, the "Ibi..." cover and binding sheets, and the Ibico calculator line.
(Just to complete the picture and muddy the waters, there is at least one other Ibico. This is Ibico Inc. of Palo Alto, California, which sells software that analyzes project schedules and task component structures, reporting on possible cost overruns and milestone creep).