Solution to Challenge 2

The crease pattern, seen from the face where the centre lines are valley folds:

 +-----------+-----------+
 |\          |          /|
 |  \        |        /  |
 |    \      |      /    |
 |      \    |    /      |
 |        \  |  /        |
 +- - - - - - X - - - - - -+
 |        /  |  \        |
 |      /    |    \      |
 |    /      |      \    |
 |  /        |        \  |
 |/          |          \|
 +-----------+-----------+

Marking the lines (this face)
- The two centre lines, one horizontal and one vertical through the middle: valley folds (dashed).
- The two diagonals, corner to corner: mountain folds (dash-dot).
- Turn the paper over and every one of these flips: the centre lines become mountains and the diagonals become valleys. That is why the answer must say which face you were looking at.

Counting on the folded base
- Flaps: four, one for each original corner of the paper.
- Layers at the open end: four sheets thick, since the paper has been folded down to a square a quarter of its original area (half the side length), with every part of the square four layers deep (check by feeling the edge).
- Closed end: the point where the centre of the paper and the folds meet, with the four corners gathered at the opposite, open end.

Checkpoint: if your drawing has all the creases but the valley and mountain labels swapped, you drew the other face. Both are right as long as you say which face you mean.