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Examples: <square>, <octahedron>.

Take $(0, 0, 0, \dots, 0)$ and flip one of 0's to $\pm 1$. Therefore has $2 \times D$ <vertices>.

Each edge E is linked to every other edge, except it's opposite -E.


Cross polytope

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<square>, cube. 4D case known as <tesseract>.

Convex hull of all $\{-1, 1\}^D$ (<Cartesian product> power) D-tuples, e.g. in <3D>:
``
( 1,  1,  1)
( 1,  1, -1)
( 1, -1,  1)
( 1, -1, -1)
(-1,  1,  1)
(-1,  1, -1)
(-1, -1,  1)
(-1, -1, -1)
``

From this we see that there are $2^D$ <vertices>.

Two <vertices> are linked iff they differ by a single number. So each vertex has D neighbors.


Ciro Santilli @cirosantilli 37

 Incoming links: Vertex