Polygonal

Blog post # 64:

Made this first picture just today.

Unintentionally Transparent


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Made this next picture about 6 years ago.

Four Times Five


Made this picture below (which is related to the picture immediately above) just yesterday.

Three Times Eight


Notice that for the 2 last pictures, there are regular polygons of m sides (m is a variable) alternating with regular polygons of n sides. Then the big polygon these smaller polygons encircle has exactly {m times n} sides.
(Squares alternating with pentagons in the first of the two pictures, triangles alternating with octagons in the last picture.
4 times 5 = 20 sides of the one larger polygon in the first of the two pictures; 3 times 8 = 24 sides of the one large polygon in the last picture.)

The only pairs (m,n) where regular polygons of m sides alternate with regular polygons of n sides AND the one regular polygon they are placed around has exactly (m times n) sides are m = 4, n = 5; and m = 3, n = 8.

There are no other such pairs of m's and n's.

Note: You can make one large regular polygon by alternating two other types of smaller regular polygons, but except for the two pairs of polygon types above, the number of sides of a type of small polygon times the number of sides of the other type of polygon will not equal the number of sides of the one large polygon they encircle.

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The latest poll has closed.

Question was: Which nonsense word do you like best?
"Thillop" wins with two votes. (It's a landslide!) "Rix", "Ryirty", and "Wuvxseoieid" each received one vote.

I should note that my own favorite 3 words were the words -- "Quune", "Estarial", and "Ostimaxillus" -- that received absolutely no votes at all.

Okay, now I have to improvise some possible definitions for "thillop".

Poll question:

Which definition do you think "thillop" should have?

1) (Noun) A type of martial-arts move involving the elbows.
2) (Noun) An obscene gesture made by making a V with the fingers of both hands, and repeatedly forcing the cusps of the V's together so that the four fingers represent two people's legs during a sex act.
3) (Noun) A type of small space vessel used by the extraterrestrials who in the future will destroy all life on Earth.
4) (Verb) To wrap an egg in polyester ribbon.
5) (Noun) A type of "spiral" that starts on the outside, proceeds to near the center, but then ends in an intermediate region.

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Leroy