The hexagons and the equilateral triangles have sides that are the same size.
Do they look the same?
The hexagons' sides look bigger but aren't really.

edit "poly

Now add the text that you can see in the picture. I've used the "set" menu to alter the font.

to poly :length :sides
repeat :sides [ fd :length rt 360/:sides]
end

Now click on the "file" menu and select "save and exit".

Now enter the command

poly 60 6

This draws a hexagon with sides that are 60 pixels long.

You can hide the turtle by typing ht. This stops it appearing in your designs.

It helps if you make another routine. This one draws a particular polygon and then moves the turtle to the correct position for drawing another polygon that is joined onto the first one.

to pv :length :sides
poly :length :sides rt 180-360/:sides
end

The pv routine has drawn an octagon and then turned through 135 degrees. It is now ready to draw something else.

pv 80 8

Thr routine has been called three times here. It has drawn an octagon, a duodecagon and a triangle. The problem is that they don't join up to make 360 degrees.

pv 40 8 pv 40 12 pv 40 3

4 squares around one vertex.

repeat 4 [ poly 100 4 rt 90]

You now need to move the turtle two full squares to the right and get it pointing upwards.

repeat 4 [ poly 100 4 rt 90] rt 90 fd 200 lt 90

Then repeat the square drawing procedure.
My program repeats the "squares around a vertex" bit three times. I've also shrunk the squares so that they don't go off the screen.

repeat 3[repeat 4[poly 50 4 rt 90] rt 90 fd 100 lt 90]

For a better way to do this and to find out how to colour the square in go to Advanced Options at the bottom of the page.

You can also tile the plane by using combinations of regular polygons. There are 8 ways that you can do this. Each vertex must have the same number of the same type of polygon and the polygons must all have the same size side.
Here is one of the patterns.

To find the other 7 patterns first find sets of polygons that can be joined together around one vertex without overlapping or leaving gaps. There are actually 17 ways that you can fit polygons together around a vertex so that they total exactly 360 degrees. Only 7 of these can tile the plan without leaving gaps. (One vertex arrangement produces two distinct tilings.

repeat 2 [poly 60 4 rt 90] poly 60 3 rt 60 poly 60 6

This code fits 2 squares, a triangle and a hexagon around one vertex. The problem is that you can't join this pattern up without leaving gaps.

Here is a pattern that will tile the plane. Can you work out how to copy it so that it joins up without leaving gaps?

poly 60 4 rt 90 poly 60 8 rt 135 poly 60 8

Real programmers work by creating objects and then joining those objects together. You should only write a piece of code once. After that you just cut and paste or work with the object.

We need to make squares and polygons with sides the same length. It also helps if we colour them in.

edit "s

Now enter this code. Remember to "save and exit" once you have put it in.

to s :size
repeat 4 [ fd :size rt 90]
pu rt 45 fd 5 setfc [0 200 0] fill bk 5 lt 45 pd
end

To run the code type:

s 100

Now if we want to make 4 squares around one vertex all you need to type is:

repeat 4 [ s 80 rt 90]

A real programmer would now make this into an object called "sv". (square vertex). So type in edit "sv and enter this code.

to sv :sz
repeat 4 [ s :sz rt 90]
end

You can then join whole blocks of squares together like this:

repeat 4 [ sv 60 rt 90 fd 120]

Here's one to get you started!

pv 40 4 pv 40 5 pv 40 20

It works because the angles of a square, pentagon and twentygon are 90, 108 and 162 degrees. These total to 360 degrees. This pattern will go all the way around the twentygon but it leaves gaps after that.