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Topic: Aristotle was Right!
Replies: 2   Last Post: Jul 12, 2010 2:22 AM

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 Kirby Urner Posts: 4,713 Registered: 12/6/04
Re: Aristotle was Right!
Posted: Jul 12, 2010 2:22 AM

Followup: D.M.Y. Sommerville documented four tetrahedral
space-fillers in his 1923 paper, Space-Filling Tetrahedra.

The Mite, and the two tetrahedral Sytes it assembles, were
three of four of them.

However the Rite also fractures into tetrahedral space-
fillers that are duplications of one another, and not made
of Mites.

Bucky Fuller never wrote about it or gave it a name,
probably did not know of Sommerville's results, which
matched his own minus this additional space-filler.

In sum:

Tetrahedral space-fillers:

Mite
Bite = Mite + Mite
Rite = Mite + Mite
1/4 Rite

Sommerville thinks these are the only four to fill
Euclidean space (by face bonding and without handedness).

The volume numbers we use in using Fuller's geometry

Basically: Mite 1/8; Bite 1/4; Rite 1/4; 1/4 Rite 1/16.

Follow-up summer reading (if you're not too bored by
spatial geometry):

http://worldgame.blogspot.com/2009/02/mite-fight.html

Kirby

Date Subject Author
6/14/10 Kirby Urner
7/9/10 Kirby Urner
7/12/10 Kirby Urner