### another self-dual space

not a projective space though

(there are “parallel lines”, for example).

ten “lines” through ten “points”.

you can get this by using

2-element subsets of {0,1,2,3,4} as points.

the lines are then triples

(like {0,1}–{1,2}–{0,2})

such that each point of the triple

is the symmetric difference

()

of the other two.

the point associated to {0,1}–{1,2}–{0,2}

in the points-to-lines correspondence

i’ve illustrated here is then {3,4}…

the complement of the union of

the three points of the line.

so you can re-create this at will.

you just have to fiddle out a

nice symmetric version of the picture.

anyhow. pick a big circle.

look at the *three* big circles

matching the dark dots inside.

the three “lines” meet at the

original point.

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March 27, 2011 at 6:05 pm

http://en.wikipedia.org/wiki/Desargues%27_theorem

March 29, 2011 at 5:36 pm

it should not go unremarked that

the points-to-lines duality for this space…

*unlike* those of the projective spaces…

is *independent* of choice-of-coördinates.

September 1, 2012 at 1:26 am

https://vlorbik.wordpress.com/2012/06/26/yet-another-duality-diagram/

big improvement.