> In geometry, how many different types of platonic solids are there?And the answer: five.The Platonic Solids (clockwise from upper left: tetrahedron, octahedron, cube,dodecahedron, and icosahedron). Photo: Armin Tavakoli via arxiv-vanity.com[https://www.arxiv-vanity.com/papers/2001.00188/].Platonic solids arethree-dimensional geometric shapes whose faces are all identical, like a pyramidor cube. There are five types of platonic solids, including the tetrahedron or4-sided pyramid, the 6-sided cube, the 8-sided octahedron, the 12-sideddodecahedron, and the icosahedron, which has 20 faces.These oh-so-friendly-sounding solids have been known since antiquity. Platohimself wrote of the solids in his famous work Timaeus. In it, Plato associatedfour of the shapes with the elements: earth was associated with the cube, airwith the octahedron, fire with the tetrahedron, and water with the icosahedron.The fifth platonic solid he associated with the cosmos. Interestingly, moderninvestigations into the shape of our universe suggest that it actually mayindeed resemble a higher-dimensional version of the dodecahedron. Whether thisrelation is fate, coincidence or some higher power...we'll let you decide. The platonic solids get their name from Plato's extensive writings on thesubject, though he was not the first to discover them. Egyptian scholars hadpublished work on the subject prior to Plato and his predecessor Pythagoras.However, Plato's work Theaetetus was the first to offer a mathematicaldescription of the platonic solids and to make the first concrete argument thatthere could only ever be five. Fun fact!Dice can only be one of the five platonic solids. Otherwise, the dice wouldnever land on a distinct face. (No dice, if you will.)