the hypercross section

[benpadiah]

http://www.benpadiah.com/basic_intro.html#hypercross

When an ordinary 3-cube is unfolded, it forms a cross of six unit squares.
So it has been reckoned that when the hypercube is unfolded, it forms a cross of eight unit cubes. Here, we see that the central cube is surrounded by six cubes, one for each side, plus a subtended eighth cube.However, this type of hypercross is comprised of eight unit cubes, while the flat cross formed by the unfolded 3-cube is only comprised of six unit squares.

Another tye of hypercross can be formed without the subtended eighth cube. Like the unfolded 3-cube, it has six cube sides around each side. This type of hypercross should not be misunderstood as lacking the eighth subtended cube, however. The eighth cube is simply hidden within this form of the hypercross, between the six surrounding cubes and the central seventh. It is what is known as an "impossible" cube. This type of impossible cube was discovered, along with a similar impossible triangle, in the 20th century by mathematician Roger Penrose. Such impossible shapes were then incorporated into the architectures depicted by Dutch artist Maurit Cornelius Escher. This type of cube is called "impossible" because it cannot exist in three space, although it can be depicted two dimensionally.

-ben
_________________

[sara]

[benpadiah]

[Guest]

The only problem with the "unfolding" is that I generally think of a cube as being solid. So how thick would it be when flattened? For that matter, how would you slice it up in order to separate the walls? Hehehehehe...

Thanks for the welcome. I don't know why more people don't drop in on you. Hope you don't mind my questions?

~ Sara

[benpadiah]