# Infill pattern comparison

I'm relatively new to 3d printing, and wanted to get a few things understood. Firstly, I am unclear on how Hexagonal infill is stronger than, say, diamond pattern.

Can anyone explain how the different shape causes the structure to be stronger? I saw a few places that hex is stronger; usually, more vertices means 'weaker' shape (i.e. a triangle is stronger than a square), so how does that work with hex vs diamond?

Also, in small objects, where the printer makes only a single dot as the infill (a dot instead of a line in larger objects), does the infill strengthen the object at all?

EDIT: I am trying to understand the effect of the infill pattern on the strength of the print, regardless of print time.

Hex grids are used for different reasons than triangular grids (such as you often see on bridges and roof systems). Triangles are especially good at being rigid, while hex grids are very material-efficient for a given strength. The second reason (\$) is typically more important for 3D printing.

Triangles do have fewer vertices than squares, but it's not always true that "fewer vertices" means stronger. Vertices are one kind of weak point. But in a triangle, vertex "angle-holding" failures simply don't matter. You can fasten 3 bars together with hinges or other joints that have little resistance to changing angle, and the triangle is still rigid.

In contrast, rectangular grids can (and do -- https://www.youtube.com/watch?v=5t9MpNTSbYg) completely collapse if their vertices aren't rigid enough. That combines badly with the fact that vertices concentrate forces, so have to be much stronger than sides in comparable settings.

A triangle cannot change without changing multiple things -- at least 2 angles and a side, or all three sides. Intuitively, the sides and vertices of a triangle work together for strength. This advantage of triangles doesn't transfer to hexagons, but hexagons have two other advantages: First, if you want to fill a space with a repeating shape, hexagons use less material than other shapes. And second, hexagons keep all the individual "walls" shorter compared to others shapes, which makes them less prone to bend.

The material efficiency was proven by Thomas Hales in 1998, according to http://www.slate.com/articles/health_and_science/science/2015/07/hexagons_are_the_most_scientifically_efficient_packing_shape_as_bee_honeycomb.html. His paper "The Honeycomb Structure" is available at https://www.communitycommons.org/wp-content/uploads/bp-attachments/14268/honey.pdf

Correction: I believe I found what you are looking for:

Report from EngineerDog.com

The author concludes that rectilinear infill with a zero degree offset is the strongest. However, I have not seen consensus for or against a certain pattern being strongest. I recommend more investigation .

I don't know that one pattern is significantly stronger than another, provided they each bond well with other infill deposits as well as the perimeters.

There are studies around. In 3D printing, strength is rarely the only consideration; one must optimize for strength where needed versus time to print.

See this as an example of a report which supports the hexagonal or honeycomb pattern as the optimal balance between strength and print time. This one is more detailed, but only compares linear infill patterns of varying layer thickness and density. There are many such articles, some more scientifically conducted than others, available with a simple search.

• This is not exactly what I meant. I will edit my question to clarify Commented Feb 21, 2017 at 19:05
• Do you want to compare different infill patterns at a certain density? Because a high density (80%) pattern A will be stronger than a low density (20%) pattern B; and as densities approach 100%, any differences will approach becoming negligible. I do not know of anything like a finite element analysis of various 3D printed infill patterns. But if you want the most strong, use the most dense: 100%.
– Davo
Commented Feb 21, 2017 at 19:44