Just imagine that you had seen a promotional product on the market but you don't know what to call it.
You know what it looks like and you know that it has a pop-up action and the only way to describe it is as a polyhedron.
Do you think that you would search the internet for "polyhedra"? No - then how about doing a search for "three dimensional solids consisting of a collection of polygons"? Hmm, maybe not.
Perhaps you might look for a "geometric object with flat faces and straight edges".
Look up "polyhedron" in Wikipedia and it tells you that Modern mathematicians do not even agree as to exactly what makes something a polyhedron, so what chance have you got of finding this certain type of product.
Cardboard engineering techniques allow only certain shapes to be made as commercially viable pop-ups and one of the most popular is based on a pentagon.
In Geometric terms this promotional pop up shape is a pentagonal dipyramid though as a Johnson solid it would be a described as a convex deltahedron - or a Johnson 13.
However, in order to make things simpler, manufacturers of such products tend to give the pop-ups much more user-friendly names and at Christmas the products are usually found on internet searches for "pop-up Christmas Decorations".
Pop up polyhedra are often used to match a company's logo but they actually lend themselves very well to being designed as a decorative piece and they have occasionally been reproduced to look like a precious stone.
The pentagonal dipyramid is not really gem-shaped but in the world of promotional pop up products the shape can be whatever you print on it! One manufacturer refers to one of its products as a pop-up diamond but the company is quick to acknowledge that it has never been printed to look like a diamond! This interactive pop-up shape is, however, best suited to being used as a promotional Christmas pop-up as it can look like a pop-up Christmas tree decoration.
The addition of a decorative loop of golden or silver string adds to the appeal of the product and makes it look even more like a Christmas decoration.
This is of particular advantage when the product is used as a company Christmas greeting as it means that the pop-up decoration will command pride of place in a customer's office as it cannot be hung on the wall ribbon with every other card.
It has 10 equilateral triangular faces so creative marketing ideas for anything that is triangular might be appropriate.
The polyhedron could also be printed look like a Halloween lantern, for example.
It has also been used successfully as a pop up mailer for product launch advertising, as a corporate event invitation and as a trade show giveaway.
So, what's in a name? To a mathematician it might be a pentagonal dipyramid but to the person looking for a promotional product it is a Pop-up Christmas Decoration, a Halloween Lantern, a corporate event invitation and a trade show giveaway.
Better still, just search for "promotional pop-ups" and keep your fingers crossed!