Most wheeled EV3 vehicles tend to have a high centre of gravity, which means the model is not as stable as it could be. I set myself the challenge of making neat models with a low centre of gravity, and here are the results. Both models are neat designs using a minimum number of pieces but with good rigidity. Both models have plenty of room at the front for attaching sensors...
The first model keeps the heavy brick very low and the vertical motors put most of the weight on the big wheels, improving their traction, but this model is not as attractive as the second. Actually this model has a fatal error if you want to program the brick through a USB cable - can you spot the problem (see later)?
The second model has an inclined brick for improved ergonomy and legibility. The inclination is based on a 9-8-4 triangle which was a nice design challenge. Note that that ratio doesn't give a perfect right triangle (try applying Pythagoras's theorem) but it's close enough to work in the real world of robotics as opposed to the perfect world of maths! The widely spaced front wheels allow the robot to turn more precisely. The disadvantages of this design include its width at the front, which would make it less than ideal for moving through a maze or between obstacles. Also, rather too much weight is over the castor rather than the driving wheels, giving the driving wheels less traction.
The third model, below, combines the features of the models above, with both vertical motors and an inclined brick (this one is based on a true right triangle with sides 13-12-5).
UPDATE: I was rather proud of these models for a brief while... until I realized that the first and third ones have a major problem. Can you spot it? It's that the 'PC' socket (needed for downloading programs to the brick via a USB cable) is very inaccessible, so these models could only work well if a Bluetooth rather than a USB connection were used. Alternatively, the brick could be turned around to 'face backwards' but I don't like models like that.
UPDATE: I noticed that a triangle with sides 4-7-8 is also (like the 4-8-9 triangle) very close to a perfect right (Pythagorean) triangle so this could also be useful in model making.