Posts tagged with topological space

Polygons (2), polyhedra (3), polychora (4-D), and polytopes (∀) can be represented as a graph — the same network-skeletal structure that models

For example, this is a skeletal graph of a cube:

So are these:

And here’s a skeletal graph of a 4-cube (tesseract).

Triangle = Blood.

And now for the news. triangular face of a polytope has the exact same topology as the blood types.

That’s weird, right?

EDIT: Oops, the bottom arrows should have been 1 → 3. Followed by 2 → 1 and 3 → 1. Also the blood-types observation is not weird, it’s just a statement of the power set topology. ‘Scuse me, while I kiss this guy.

Blood types form a topological space (and a complete distributive lattice). There are three generators: A, B, and Rh+.

Above the “zero element” is the universal donor O− and the “unit element” is the universal receiver AB+.

A topological space contains a zero object, maybe other objects, and all unions & intersections  of anything in the space.  So taking the power set  of {A, B, +} yields the “power set topology” which I drew above. AB+ is the 1 object and “nullset” O− is the 0 object.

A lattice has joins  & meets  which function like  and  in a topological space. Like 1 or True in a Heyting algebra, blood type as a power-set topology has one “master” object AB+.