{c}
{wiki}

A <Cartesian product> that carries over some extra structure of the input groups.

E.g. the <direct product of groups> carries over <group> structure on both sides.


Direct product

{wiki}

<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 35

 Incoming links: Cartesian product