In Jacobs Geometry Chapter 15 Lesson 1 problem 57, we are asked,

“In how many planes do the square faces of the cube faces of the unfolded hypercube lie?”

The Solutions Manual says 13 planes. Let’s see how they got that number.

Imagine the red, yellow, and blue lines drawn on the hypercube as planes.

Counting vertical planes from right to left: marked in red we have 5.

Counting vertical planes from front to back: marked in yellow we have 4.

Counting horizontal planes from bottom to top: marked in blue we have 4.

5 + 4 + 4 = 13 planes.

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