3 Non-Parallel Planes divide Space into 8

Theorem

Let $3$ planes which are pairwise non-parallel be constructed in ordinary $3$-dimensional space.


Then that space is divided into $8$ parts by those planes.


Proof


This theorem requires a proof.
In particular: Intuitively obvious but needs a run-up
It's not actually even true -- consider the case where all $3$ lines of intersection of the $3$ planes are parallel. Needs to be reworded, presumably just means the lines of intersection are pairwise non-parallel as well.
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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$
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