Okay kiddo, have you ever played with blocks and noticed that they fit together in different ways? That's kinda like what crystals are - but super tiny! Crystals are made of atoms and molecules that fit together in a certain pattern to make a solid shape.
Scientists study these crystal patterns, and they call it crystallography. There are different types of patterns, and some of them are called "Euclidean." That's a big word, but it just means they follow the same rules you learned in math class - like how a square has four sides and four angles that add up to 360 degrees.
But sometimes, the crystal patterns don't follow those same rules. They're called "non-Euclidean." It's like playing with blocks that don't fit together in a straight line, but curve or twist in different ways.
Scientists who study these unusual crystal patterns use something called a "non-Euclidean crystallographic group" to describe them. It's like a set of rules that explains how the crystal pattern works.
So, to sum it up, a non-Euclidean crystallographic group is a way that scientists describe the pattern of atoms and molecules in a crystal when it doesn't follow the same rules as most crystals. It's like describing how blocks fit together when they don't make a straight line!