A Definition and Comparison to the Archimedean Solids

We want to define a platonic solid in this video. And we’ll look at what is and what is not a platonic solid. We’ve already seen in the last video, there are in fact, five. But let’s have a look at the rules. Well, every face is the same regular polygon. And the same number of faces meet at each vertex. So I can then ask you, is this a platonic solid? And the answer is no. It’s faces A different How about this one? No, it’s faces are different. It happens to be a square pyramid. How about this one? No, it’s faces are different. This one is interesting. Its faces are the same, but by are not regular polygons. So it’s not a platonic solid football. Well, is that a platonic solid? No, as you can see from the model, its faces are different. But it is what’s called an archimedean solid. Archimedes, of course was a Greek mathematician. So what is an archimedean solid? Well, the faces are different regular polygons. And the same set of polygons meet at each vertex in the same pattern. So let’s have a look at some of these. We’ll bring back the football. It’s a truncated icosahedron. It is an archimedean solid. Why? Because it has two regular hexagons and one regular pentagon at each vertex Is this one an archimedean solid? Yes, it has one regular Decker gone one square and one regular hexagon at each vertex and this one yes it has three squares and one equal actual triangle at each vertex. This is also an archimedean solid it has one regular pentagon and four equal lateral triangles at each vertex This one, yes it has one square and four equal lateral triangles and each vertex. Finally, yes, it has two regular deca guns and one equal lateral triangle at each vertex. There are all 13 archimedean solids all with different names. And as we’ve seen before, there are five platonic solids plus 13 archimedean solids, that’s a total of 18 solids. Now we know what a platonic solid is and an archimedean solid Now you recall there are five platonic solids. But why are there only five? Well, the answer is because only five are possible. And in the next video that’s what I’ll explain.