The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.pre-college

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Aristotle was Right!
Posted: Jul 12, 2010 2:22 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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:

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):


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.