Goldberg–Coxeter construction
Okay so imagine you have a bunch of sticks that you can connect together at their ends. You can make different shapes by connecting the sticks in different ways.
Now, let me introduce you to something called a polyhedron. It's a 3-dimensional shape made up of a bunch of planes. Like a box, or a pyramid.
The Goldberg-Coxeter construction is a way we can make new polyhedra based on some rules. We start with a polyhedra that has only one type of plane.
First, we pick a plane on the polyhedra and imagine it's like a window. We then fill this window with more sticks to make a new shape. We keep doing this until we get a new polyhedron that has more than one type of plane.
This process involves a lot of math, but the idea is that we are adding more complexity to the shape by adding new windows and filling them with sticks.
So, to summarize, the Goldberg-Coxeter construction is a way to make new polyhedra by adding new windows to a shape and filling them with sticks. This process results in more complex and interesting shapes.
Now, let me introduce you to something called a polyhedron. It's a 3-dimensional shape made up of a bunch of planes. Like a box, or a pyramid.
The Goldberg-Coxeter construction is a way we can make new polyhedra based on some rules. We start with a polyhedra that has only one type of plane.
First, we pick a plane on the polyhedra and imagine it's like a window. We then fill this window with more sticks to make a new shape. We keep doing this until we get a new polyhedron that has more than one type of plane.
This process involves a lot of math, but the idea is that we are adding more complexity to the shape by adding new windows and filling them with sticks.
So, to summarize, the Goldberg-Coxeter construction is a way to make new polyhedra by adding new windows to a shape and filling them with sticks. This process results in more complex and interesting shapes.