Below we have an image of a rhombic dodecahedron cut according to the B3 hyperplane arrangement, resulting in 48 cells (= 4 x 12 faces) that correspond to elements of the Weyl group. Another way of thinking about this image is that it is the union of the (closures of) the alcoves neighboring the origin in affine B3.
To build the type B3 Steinberg torus, we identify opposite faces of this subdivided polyhedron.