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Math 6510 • Differentiable Manifolds

Fall 2002 • Question 15

The 4-dimensional cube \([0,1]\times [0,1]\times [0,1]\times [0,1]\) has 16 vertices, 32 edges and 24 2-dimensional faces. How many 3-dimensional faces does it have?

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The 4-dimensional cube \([0,1]\times[0,1]\times[0,1]\times[0,1]\) has 16 vertices,
32 edges and 24 2-dimensional faces. How many 3-dimensional faces does it have?