The idea that glass forms crystals that are 5-sided in 2 dimensions, and icsosahedral in three isn't very useful for most people trying to understand why glass does what it does.

So, let's work in 2 dimensions.

Think about this like tiling a floor - the formal name for this is tessellation theory.

It's easy to tile a floor with squares. It wouldn't be too hard with rectangles either.

The reason for this is that if you put two squares next to each other, the 90 degree angle in the bottom right of the left one, and the 90 degree angle in the bottom left of the right one, join together to form a 180 degree angle - a straight line. Continue that across the floor and you've got a good start on covering the whole floor.

It turns out you can also do this with certain triangles. Right triangles are easy: no matter what the size, you can stack two of them to get a rectangle, and off you go.

Equilateral triangles will also work - you just alternate them right-side-up and upside-down. If you put 3 of them together this way, you get a regular trapezoid, because in the middle of the bottom of the trapezoid are three 60 degree angles that add up to 180. You could also tile a floor with rhombuses formed from putting 2 equilateral triangles next to each other.

You can also cover a floor with hexagons (anyone who played board wargames will tell you this). The problem is that you need half hexagons on the borders. Think about it: if you take the top half of one hexagon, and put the bottom half of another one next to it, they will fit together perfectly. This is because regular hexagons can actually be broken down into 6 equilateral triangles, with each face of the hexagon the base of a triangle pointing inward.

The reason all of this works is a theorem from plane geometry that the interior angles of n-sided regular polygons are given by 180 times n-2 divided by n. For an equilateral triangle this works out to 180 times 1 divided by 3 is 60. For a square, it is 180 times 2 divided by 4, is 90.

In order to cover a floor you have to be able to get r of those angles to add up to 180 (where r is an integer). So, we have:

180r(n-2)/n = 180

r(n-2) = n

So, we can cover a floor with equilateral triangles because:

3(3-2) = 3

Same for squares (this shouldn't be surprising because they can be made out by combining triangles):

2(4-2)=4

You can even get an idea of why you need half-hexagons to cover a floor with them since 3 times (6-2) does not equal 6 (but it does equal 2 times 6).

More importantly, this tells us why pentagons won't work since:

r(5-2)=5

Does not have an integer solution for r.

So, in 2 dimensions, glass sort of acts like a Tetris game in which the shapes are not built out of squares but out of pentagons. You can probably envision that this means there will be a lot of empty spaces left between shapes.

It's harder to visualize extending this to 3 dimensions, but the basic point follows that there will be "holes" in between the crystals within glass that just aren't there in other solids. Since there are holes, there will sometimes be movements of crystals from one spot to another to fill those holes - thus the liquid properties of glass. Alternatively, those spiky crystals won't move much no matter how many holes there are - thus the solid properties of glass.

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