adobe illustrator - How to create perfect geometric triangle seamless pattern

I'm trying to create a seamless triangle repeat pattern like this:

http://www.redbubble.com/people/bakmannart/works/15661602-my-first-exploring

(sorry, I can't seem to get the image to actually be in this page as it's from RedBubble). However, without these colours necessarily, just the seamless, accurate, geometric pattern; using what is known as the 'triforce' from Legend of Zelda (3 triangles - or 4, depending how you consider it - form together to make one larger triangle). I'm fairly new to Illustrator, however I've tried a few things:

1. creating a perfect triangle using polygon tool. rotate/copying the triangle into a 'triforce' shape. There is always a few points difference though, likely because i'm terrible at maths



2. 
   

   trying this tutorial. however, I often get stuck with the line/stroke where the paths of the grid intersect to from triangles. unlike the video's at 3:05 mins, the lines on my work are thicker in some places and basically vary in length.considering i'm using the shape builder tool( as the tutorial denotes to do )it might create some sever inaccuracy in terms of shapes later on. (sorry I can't provide a picture, not enough reputation!)

   
   


3. 
   

   I've tried just using the move tool and smart guides/locking or whatever it is to accurately position triangles together. I don't know how reliable this is, though - and then I have to work out what shape to create (e.g hexagon, square) that will repeat well.

   
   

Any ideas? I feel like I'm missing a really simple method. Thank you so much in advance!