Two students in my class asked and answered what might be a novel question. It is well known that the cube has exactly $11$ edge-unfoldings (or "nets"), as shown below:

(Image from this MO posting.)

It is also well known that each of the eleven can tile the plane,
i.e., form a *monohedral* tiling.
The students,
Elsa Bieger and Heather Robertson,
asked: Can the $11$ unfoldings be edge-to-edge glued together, each used
exactly once, to form a *supertile* that can then tile the plane
monohedrally?
They found four supertiles:

and here's how each supertile fits together with copies of itself:

So in the spirt of the earlier MO question, Which unfoldings of the hypercube tile 3-space, which led to Moritz Firsching showing that all hypercube unfoldings can (individually) tile space, it is natural to ask:

. Can the $261$ unfoldings of the hypercube be face-to-face glued together, each used exactly once, to form a supertile that can then tile $3$-space monohedrally?Q