The What-the-heck-ahedron was made by the creators of other 3D puzzles, like the "Stressaract" and the "Annoyangle."
Dipper purchases a copy of the puzzle in the "Little Gift Shop of Horrors" segment "Abaconings," attempting to solve it and earn his image on the back of the box. After failing it several times, he becomes frustrated and decides to resort to supernatural means. While looking through his journal, he discovers the Percepshrooms that exist near Lake Gravity Falls, and intends to use them to acquire a higher intelligence. However, Waddles consumes them before they can reach their full effect. Dipper awakes to find the What-the-heck-ahedron already completed by Waddles, who is now incredibly intelligent from eating the Percepshrooms. Waddles spits it out after he re-sizes his IQ at the end of Stan's story.
The What-the-heck-ahedron appears to be a ball surrounded by three rings when solved. The shape's color consists of multiple types of purples and blues, all separated by lined patterns surrounding the object's exterior.
The packaging is labeled with the puzzle's name at the top with an image of a completed puzzle at the bottom. Underneath is a line of text attributing other puzzles the product's creators have designed. The back of the box explains that whoever is able to complete the What-the-heck-a-hedron will be featured in a photo on the packaging. A picture of a previous winner (being kissed by a woman in a red leotard) is seen as well, labeled "Winner!" in large font.