Example: What happens when we start adding up odd numbers? 1=1, 1+3=4

Each higher-dimensional figure is built by taking two copies of the previous figure and connecting corresponding dots with edges.

The number of vertices $V_n$ in the $n$-dimensional figure satisfies:

For $n=1$: $V_1 = 2 \cdot V_0 = 2 \cdot 1 = 2$
For $n=2$: $V_2 = 2 \cdot V_1 = 2 \cdot 2 = 4$
For $n=3$: $V_3 = 2 \cdot V_2 = 2 \cdot 4 = 8$
For $n=4$: $V_4 = 2 \cdot V_3 = 2 \cdot 8 = 16$

Unrolling the recursion:

For the 5-dimensional figure, the number of vertices is $V_5 = 2^5$.

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