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A cube in this case is a 4 dimensional object which can be represented by a 4 dimensional vector having components (v1,v2,v3,v4). Each component or element of this vector can exist in 2 states (at either end of the line, or side of the face) therefore there are 2 possible places in space that each component can occupy. Sincere there are 4 vectors, there are 2*2*2*2 possible combinations or 2^4 = 16 corners

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Q: How many corners does a cube have in 4 dimensions?
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