1. Two big parallel triangles in the cube.
2. This configuration is the same as configuration 1, except that the red and blue triangles have been moved. There are now four planes of triangles in the cube. As in answer 1, all the triangles are parallel.
3. Four of the triangles touch each other at the center, and another four touch in a ring around the center.
4. This configuration is the same as configuration 3, except that each triangle has been turned upside down. Four triangles on the inside form every other face of an octahedron around the center. Four others hover outside the missing faces of the octahedron.
1. Surprisingly, a cut down the middle gives you a single loop of paper instead of two. The loop now has three twists. 2. You need two trains. The two parallel tracks traverse "both" sides of the Möbius strip, then return to their original points. 3. You end up with two loops. The middle third remains an ordinary Möbius strip, and the outer two-thirds of the loop forms a second, double-length loop linked to the first loop. 4.
One train: Two trains (or glue the ends to make two Möbius strips):
Three trains:Four trains:
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