A cube of cheese
\[C = \{(x,y,z) : 0 \le x, y, z \le 1\}\]is cut along the planes $x = y,$ $y = z,$ and $z = x.$  How many pieces are there?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A cube of cheese
\[C = \{(x,y,z) : 0 \le x, y, z \le 1\}\]is cut along the planes $x = y,$ $y = z,$ and $z = x.$  How many pieces are there?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
A cube of cheese
\[C = \{(x,y,z) : 0 \le x, y, z \le 1\}\]is cut along the planes $x = y,$ $y = z,$ and $z = x.$  How many pieces are there?
train