From rob@twcny.rr.com Mon Sep 10 21:10:09 2001 Return-Path: X-Sender: rob@twcny.rr.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_2_1); 11 Sep 2001 04:10:08 -0000 Received: (qmail 75897 invoked from network); 11 Sep 2001 03:59:35 -0000 Received: from unknown (10.1.10.27) by l9.egroups.com with QMQP; 11 Sep 2001 03:59:35 -0000 Received: from unknown (HELO mailout5.nyroc.rr.com) (24.92.226.122) by mta2 with SMTP; 11 Sep 2001 03:59:21 -0000 Received: from mail1.twcny.rr.com (mail1-1 [24.92.226.139]) by mailout5.nyroc.rr.com (8.11.6/Road Runner 1.12) with ESMTP id f8B3w8427151 for ; Mon, 10 Sep 2001 23:58:08 -0400 (EDT) Received: from riff ([24.92.246.4]) by mail1.twcny.rr.com (Post.Office MTA v3.5.3 release 223 ID# 0-59787U250000L250000S0V35) with ESMTP id com for ; Mon, 10 Sep 2001 23:57:02 -0400 Received: from rob by riff with local (Exim 3.32 #1 (Debian)) id 15gegC-0003a8-00 for ; Mon, 10 Sep 2001 23:57:44 -0400 Date: Mon, 10 Sep 2001 23:57:44 -0400 To: lojban@yahoogroups.com Subject: Re: [lojban] Polyhedra Message-ID: <20010910235744.A13715@twcny.rr.com> Reply-To: rob@twcny.rr.com References: <9njo3g+hmjs@eGroups.com> <0109102149400I.05004@neofelis> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <0109102149400I.05004@neofelis> User-Agent: Mutt/1.3.20i X-Is-It-Not-Nifty: www.sluggy.com From: Rob Speer On Mon, Sep 10, 2001 at 09:49:40PM -0400, Pierre Abbat wrote: > On Monday 10 September 2001 21:06, tupper@peda.com wrote: > > Are the names of any polyhedra besides "cube" available in > > Lojban? The tetrahedron is another important polyhedron that > > also has analogues in other dimensions. > > Triangles and tetrahedra are called simplexes, so I suggest sapkubli be li ny > for n-dimensional simplex. Squares, cubes, and tesseracts are kurkubli be li > ny. Tilted squares, octahedra, etc. might be called dutkurkubli be li ny; > they are the duals of their respective kurkubli. > > La'edi'u are the only regular kubli be li su'o 5. The others in 3d are the > icosahedron and dodecahedron; in 4d there are a solid with (IIRR) 120 > tetrahedral faces which meet 20 at a corner, a solid with dodecahedral faces > which meet four at a corner (dual of the preceding), and one with 24 > octahedral faces, which is its own dual. > > Then there are cuboctahedra, rhombic dodecahedra (dual of CO), and assorted > other semiregular polyhedra. You don't even need all the separate names. All of this is accounted for in the place structure of {kubli}. For example, a regular N-gon would be {kubli be li re bei li ny.} You could even use lujvo: {fo'arkubli} = x1 is a regular fo'a-dimensional polygon with x2 [fo'a - 1]-dimensional surfaces. (relkubli, cibykubli, vonkubli...) Then you have: pavykubli ("line segment": its surfaces are the two endpoints) relkubli be li ny. (to ny. zmadu li re toi) cibykubli be li 4 .a li 6 .a li 8 .a li 12 .a li 20 vonkubli be li 5 .a li 8 .a li 16 .a li 24 .a li 120 .a li 600 However, since in higher dimensions than 4 the shapes are better described by their relation to each other than their number of sides, the suggestions you made would fit there. -- Rob Speer