#minkowski sum

[birdthatlookslikeastick]

hey tumblr i made a gif again

[isomorphismes]

Minkowski sum of two shapes

direct product of two shapes

two complementary planes in 4-D will only intersect at the origin

(polytopes are higher-dimensional polygons … not necessarily regular and they can even go backwards into themselves. Basically a filled-in shape cut out by straight or flat lines/planes/hyperplanes.. So think for example most of the boundary conditions in optimisation. (I usually see something like: a convex function, restricted to a filled-in irregular convex polytope, eg ◣ ⏢ or ◺ ▲ ▶ ◆ , ▷ or ⬠ ⬟ ⌂ 🏠 or a ☖ ☗ ⛊ ⏢ ⬡

(non-polytopes in the Unicode sets where I was searching for those include ◫, ◙, ◶, ▤, ▣, ◐, ◠, ⍟, ⌫, ⌻, ⌘, ⌧, ⌰, ⌑, ⍉, ⍋, ⍾, ⎎, ⎍, ⎌, ⏪, ⏚

You can make a convex polytope from ∩ of half-spaces, or from a convex-hull of vertices.