Simplicial complex

A simplicial complex is a fancy way of talking about shapes that are made up of simple pieces. Imagine you have a bunch of different colored blocks, and you want to use them to build a bigger shape. You can only use the basic shapes, like triangles and squares.

A simplicial complex is kind of like building with blocks, but instead of blocks, we use these simple shapes called "simplices." A simplex is just a basic shape, like a point (which is just one dot), a line (which connects two dots), a triangle (which has three sides), or higher dimensional shapes like a tetrahedron, octahedron, etc.

We can take these simplices and stick them together to create shapes. For example, we can take two triangles and connect them at one side to make a square. We can also take four triangles and connect them at the corners to make a pyramid with a triangular base.

So a simplicial complex is just a bunch of these simple shapes stuck together in different ways to create more complex shapes. Think of it like building a puzzle, but instead of using puzzle pieces, you're using simple shapes like triangles and squares.