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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: 4,709
Registered: 12/6/04
Re: Aristotle was Right!
Posted: Jul 12, 2010 2:22 AM
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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
are discussed in linked resources.

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



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