Abstract polytope

Okay kiddo, let me explain what an abstract polytope is. Imagine you have some toys like blocks and balls. You like to play with them and build different shapes using them. Now, Let's say you have a new toy that is a magic shape. You can see it in your mind, but you can't touch it with your hands. That's what an abstract polytope is. It's a shape you can't touch, but you can imagine in your mind.

An abstract polytope is a geometric object, just like a shape made out of blocks or other toys. But, instead of being made of physical materials like plastic or wood, it's made up of groups of numbers and lines that describe the shape. Think of it like a blueprint or a map.

To make it easier to understand, let's look at an example. Think of a triangle. You can draw a triangle by connecting three points with lines. But in an abstract polytope, we don't need to draw it or see it physically. We can just use math to describe it. We use numbers and equations to show how the shape is built.

Abstract polytopes can have any number of sides, which we call dimensions. You can make a two-dimensional polytope, like a flat shape or a three-dimensional polytope like a cube. They can also have different numbers of sides or faces. Polytopes can be complex objects, and mathematicians find them fascinating to study.

In summary kiddo, an abstract polytope is like a special toy made of numbers, lines, and equations. You can't touch them or see them, but they exist in our imagination, and mathematicians use them to explore new ideas and solve problems. It's like playing with your toys, but instead of blocks and balls, you’re playing with numbers and shapes. Pretty cool, huh?