Make your own paper orthogonal permutohedron! Here's how. Print out the pattern, cut the solid lines, valley fold the dashed lines, and mountain fold the dash-dot lines. (I used a box-cutter both to make the cuts and to prescore the folds.) Here's what it looks like when you're done:
See also this fractal staircase, another orthogonal polyhedron constructed in a similar way.
I am suddenly reminded to dig out the exacto knife and start on the Christmas cards.
My wife said something similar when she saw this.
Of course you should draw your own pattern not print one :P
I drew it. On the computer. And then I printed it. Of course, if you want a different orthogonal polyhedron than this one, you'll have to draw your own, but I hope the pattern for how to draw it is clear enough from this example.