From <@UBVM.CC.BUFFALO.EDU:owner-LISTSERV@UBVM.CC.BUFFALO.EDU> Sun Feb 5 03:20:03 1995 Received: from netaxs.com (root@netaxs.com [198.69.186.1]) by access.netaxs.com (8.6.9/8.6.9) with ESMTP id DAA08659 for ; Sun, 5 Feb 1995 03:20:03 -0500 Received: from UBVM.cc.buffalo.edu (ubvm.cc.buffalo.edu [128.205.2.1]) by netaxs.com (8.6.9/8.6.9) with SMTP id DAA02954 for ; Sun, 5 Feb 1995 03:20:02 -0500 Message-Id: <199502050820.DAA02954@netaxs.com> Received: from UBVM.CC.BUFFALO.EDU by UBVM.cc.buffalo.edu (IBM VM SMTP V2R2) with BSMTP id 7972; Sun, 05 Feb 95 03:19:42 EST Received: from UBVM.CC.BUFFALO.EDU (NJE origin LISTSERV@UBVM) by UBVM.CC.BUFFALO.EDU (LMail V1.2a/1.8a) with BSMTP id 3768; Sun, 5 Feb 1995 03:19:42 -0500 Date: Sun, 5 Feb 1995 03:19:39 -0500 From: "L-Soft list server at UBVM (1.8a)" Subject: File: "GEODESIC LOG9307" To: "Christopher J. Fearnley" Status: RO ========================================================================= Date: Sun, 11 Jul 1993 13:04:14 PDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 4D Solutions Subject: Re: Synergetics II The Buckminster Fuller Institute in LA may be able to help you get Synergetics II -- you may have tried them already. I only see Synergetics listed in their catalog. Tel: 310 837 7710 ========================================================================= Date: Sun, 11 Jul 1993 15:22:19 PDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 4D Solutions Subject: buckyball algorithms > I am looking for an algorithm to generate the coordinates > for n equally spaced points on the surface of a sphere, for > arbitrary values of n. > Are all vertices of a buckyball equally spaced? > What is an algorithm for generating the coordinates > of the vertices? How much variety is there in shapes > for geodesic domes (that is, if I want to tessellate > a sphere with n points, what are my choices of n if I use > buckyball-like structures)? > Thank you for your help, > DanLip > (E-mail responses would be appreciated. Thank you.) > danlip@cns.caltech.edu Re: buckyballs, n point equi-spaced spherical distributions The edges of a geodesic dome are *not* all the same length. The angstrom measurements between neighboring carbon atoms in a fullerene are likewise not equal. Domes come in three Classes (I, II and III). The classification system has to do with laying an equilateral triangle down on a grid of smaller equilateral triangles, lining up corners with corners -- either aligning the triangle with the grid (I), turning it 90 degrees to bisect grid triangles (II), or rotating it discretely to have it cut skewly across the grid (III). 20 of these triangles make an icosahedron which is then placed within a circumscribing sphere. The vertexes of the triangles' internal points, defined by the grid pattern, define radii with the circumscribing sphere's center. By pushing each vertex further out along the segments so defined, until each is made equidistant from the center, an omnitriangulated geodesic sphere is formed (orthonormal projection I think cartographers call this). Again, resulting surface edge lengths are not all the same length. The resulting mesh will always contain 12 sets of 5 triangles organized into pentagons, the rest into hexagons. The Class I version of the algorithm above always creates 20F^2 surface facets where F=1 gives the icosahedron itself. The external point population will be 10F^2+2. Since points plus facets = edges plus 2 (Euler), you will get 30F^2 edges. F is what Fuller called the Frequency of the geodesic sphere and, in the Class I case, corresponds to the number of grid intervals along any one of the 20 triangle edges. Note: "buckyballs" in the sense of "fullerenes" are not omnitriangulated (the edges internal to the 12 pentagons and n hexagons have been removed) and come in infinitely more varieties than the above algorithm allows. The above algorithm is limited to generating point groups with icosahedral symmetry -- a minority of the fullerenes are symmetrical in this way, although C60, the most prevalent, is a derivative of the Class I structure. Kirby Urner pdx4d@igc.apc.org l ========================================================================= Date: Sun, 11 Jul 1993 15:24:34 PDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 4D Solutions Subject: optical properties > Also, has anyone info on using (buckminster) Fullerines (with > one atom-different element floating inside) being used in > optical applications?? I just returned from Fullerenes '93 (June 27- July 1), a multi- disciplinary conference on the fullerenes in Santa Barbara. Both principal fullerene co-discoverers (Kroto and Smalley) were present. Unfortunately, I am not a chemist and a lot of the talk was hard for a layman to follow, but I think I can vouch for the accuracy of the following: Fullerenes with atoms or clusters of atoms inside, the so-called "endohedral fullerenes", are presently extremely difficult to isolate in quantity and their properties are as yet poorly understood (no one yet knows, for example, if crystals of same will superconduct, as does K3C60 -- potassium atoms in all the intersticies in a C60 crystal packing). The suggested notation for endohedrals, by the way, is X@Cn, e.g. K@C60 (potassium atom inside C60). Endohedrals aside, however, plain ol' hollow buckminsterfullerene (C60) is becoming ever easier to get in quantity and shows many interesting optical properties. It stops light -- the brighter the light the more effectively it stops it. Nano and pico-second laser pulses are effectively and instantly opaqued by small quantities of C60. Putting it in goggles or welders' masks is a definite possibility (Patterson AFB in Ohio is studying such applications). Many other optical properties of the fullerenes are under study and a whole conference on the topic is coming up (in San Diego I think). However, C60 remains forty times more expensive than gold. As Smalley put it "it's the yield, stupid" -- i.e. the central issue facing fullerene researchers, in Smalley's opinion, is how to get more of it. The Smalley team approach of using parabolic mirrors to sun-generate fullerenes (to produce "sunnyballs") appears to be a potentially promising approach. Concentrated sunlight has less of the damaging frequencies in high-powered lasers that apparently to inhibit fullerene formation from vaporized carbon). Kirby Urner pdx4d@igc.apc.org ========================================================================= Date: Mon, 12 Jul 1993 00:04:23 EST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works Comments: Warning -- original Sender: tag was NETNEWS@AUVM.AMERICAN.EDU From: scimatec5@UOFT02.UTOLEDO.EDU Organization: University of Toledo, Computer Services Subject: Math equation for geodesic dome Does anyone know of a book I can get with the mathmatical equations for designing a geodesic dome. Thanks, Steve Mather ========================================================================= Date: Tue, 13 Jul 1993 03:17:31 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chris Fearnley Subject: Re: Math equation for geodesic dome In-Reply-To: Message of Mon, 12 Jul 1993 00:04:23 EST from Hugh Kenner's book I think it's titled: _Geodesic Math and how to use it_ would serve. But all you really need to know is spherical trigonometry. See Fuller's magnum opus _Synergetics_ in vol. 1 sec. 457.00-459.03 provides much of the spherical relationships and vol. 2 sec 1052.00-1050.44 and color plate 1 give Napier's rules for calculating the spherical trig data. It's real ly rather simple. Good Luck! ========================================================================= Date: Sat, 31 Jul 1993 18:51:25 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Michael Norelli Subject: Ed Applewhite Does anyone know is Ed Applewhite, the collaborator with Bucky on Synergetics, is still alive? Last I heard he was in Washington, D.C... Thanks