Below we see the type G2 Steinberg torus. It is formed by identifying opposite sides of a hexagon that has been cut into twelve right triangles gotten by drawing lines between opposite vertices and midpoints of opposite sides. Another way of thinking about it is that we've bisected all the angles in the A2 picture (indicated with green lines).
This region is the union of the (closure of the) alcoves neighboring the origin in affine G2.