[3] is left as an exercise

Photo on 4-24-15 at 12.36 PM

the colors-to-corners assignment here
is nonstandard… i.e., inconsistent
with the one i’ve been using as my
“base case” in earlier blog entries.

so for heck sake don’t memorize ’em this way.

the “algebraic” aspect here…
whereby certain “vertex triples” are assigned
“dual vectors” according to the scheme
[1] = [0:0:1] —> {010, 100, 110}
[2] = [0:1:0] —> {001, 100, 101}

[7] = [1:1:1] —> {011, 101, 110}…
isn’t affected by my having “renamed the colors”.

some mod two equations are included.
this justifies the orientation-reversal
in [7]. it’s still a pretty lousy draw-
ing, though.

“mod two arithmetic” underlies our whole
algebraic “scheme” (*not* a technical term here):
the duality constructed here will turn out to be
“the *dot product* (mod two)” when our scheme has
been fully carried out.

also i don’t vouch for the stuff in pencil.
i drew this a few years ago and’ve only
checked the parts i inked in today.


  1. Photo on 4-24-15 at 11.45 PM

    okay, you win. i found this
    (pencils only) answer
    in the back of the book.
    okay, a few pages later,
    still in the middle of the book.
    okay, the moleskin.
    anyway, there it is. i think.

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