In China, 8 is considered lucky. Relating to that, here are four puzzles based around the 8-cornered cube.
A. Arrange the numbers 1-8 on the corners so that the 6 faces have magic sum 18.
B. Arrange the numbers 0-7 on the corners so that the connecting edge always has a prime sum.
C. Arrange the numbers 1-12 on the edges so that faces and parallel edges have magic sum 26.
D. Arrange the numbers 1-12 on the edges and (0,1,2,3,4,7,9,12) on the corners so that each edge gives the difference between the corners it connects.