only by routing around “the improved posting experience” am i able to do this at all; moreover i can only find the route by dumb luck. quit moving the damn cheese, i beg of you, wordpress. but wordpress has outsourced the legacy stuff to some pay-no-mind LLC or something.

Photo on 11-17-15 at 10.46 AM

saturday night i colored in the corners of this cube.
the underlying black-and-white is based on a work of
the great dutch artist m.~c.~escher. the cardboard
cut-out version is from a collection by the american
mathematician doris schattschneider.
(_m.c._escher_kaleidocycles_).

anyhow, i’ve had the whole “5 platonic solids” set
from this work on display in the front room at home
for a while. the others are in color already, right
out of the book. i’ve had *another* set of these,
too: it’s a great “book” and might still be in print
for all i know. i had two editions, from years apart,
years ago.

i took this one to church on sunday and used it in my talk.
there wasn’t time to explain why i’d colored it the way i
did. but i *did* count the symmetry group of the cube,
two ways. any talk by me should have a theorem in it;
i’m happy to count that as a theorem.

24 because any of the 6 faces can be “face down”,
and each such choice-of-face allows for any of 4
remaining faces then to “face front” (all but the
“face-up” one *opposite* to our “chosen” face).

but also 24 because
1 identity
6 180-degree “flips” that fix two edges
(one for each pair of opposite edges)
8 120-degree “corner-turns”
(fix a pair of opposite corners;
there are 4 such; one may “turn”
right or left)
6 90-degree “face turns”
(fix opposite faces—3 ways; again,
one can go “right” or “left”)
3 180-degree face turns.

and this messy version is actually quite clear when
one is actually holding up an actual cube and pointing
at the drawing on the board. or in this case, at one’s
own sweatshirt. canvas makes a good whiteboard.

you can do it all without even mentioning “group theory”…
and i *sure* didn’t get to prove that this set of 24
“moves” gives a version of “the symmetric group on 4
objects”. anyway, part of the point is that one need
not have introduced any “math code” into the discussion
at all to arrive some some *very* useful results.

i learned the symmetry-groups-of-solids trick from an
old master
. i mentioned this book in the service.

but mostly i talked about stuff like bible studies and music.

stuff that people actually show up at church *for*. bring what
you love to church and share it. food and money are particularly
welcome.

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