Well, Escher Triangle usually is represented with 3 colors, one for each "plane", and yours has only 2. I think maybe you could start with that.
Also If you want to try dithering you can shape shadows like that; this will be more difficult so more interesting (?).
About your pixelart technique, I have some things to say. Look your outlines and birkka's, and compare: yours in some parts are double, that is what some pixelartists call "banding" and you should try to skip it. Do antialias, not banding. It's not the same (sometimes banding is inevitable but you can hide it a little, breaking that big pixels)
Also, the use of 2 different colors for outline made you do some selout. I will no tell you a lot about selout because someone could shoot me; some pixelartists are in favor of using selout and others extremely not (it's like a taboo word but you deserve to know what it is). I think it's because they tell about different thinks and call it always "selout".
The people who is pro-selout talk about breaking the outline a little to fit better with an specific background that will have always more or less the same darkness (so "selout" in that case makes the sprite and the background fit better)
Look the outlines of that girl, it's "good selout", on white maybe looks strange but the background of the game is dark-brown to not-so-dark-brown and it always looks good xD
The people who is against selout talk about giving the outline some lightness effects so in light parts the outline is bright and in dark parts no (and they call it "selout" or simply "shit"). That's not the same, that "bad selout" makes the sprite not fit well with any background because when some part looks well the other parts look weird and conversely. They say also a big truth; when you make that selout you break the shadow forms (especially with dark background colors)
What I can say to you is:
Make "good selout" if you want but try never to do "bad selout". If you aren't sure what type of selout you made, just don't use it xDAnd also:
Don't talk so much about selout. I am putting myself in danger now.
