It is a really cool shape. An orthoplex is a type of shape which exists in every dimension and is my favorite. The points that define it are every permutation of (1[+ or -],0,0,...0). So a 2-D orthoplex's points have the coordinates (1,0), (-1,0), (0,1), and (0,-1), which is a square. A 3-D orthoplex's points have the coordinates (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), and (0,0,-1), which is an octahedron. The 4-D orthoplex is called a 16-cell or hexadecachoron and you can find you-tube videos that show shadows of this. Thanks for writing the poem!