... Yes. That is how I worked out the mid-point of the face of the tetrahedron. This tetrahedron is sitting in a 2F cube of edge (.707). One of those eight...
6802
Alan M
a.michelson
Apr 10, 2012 7:24 pm
... 1.2 ???...
6803
Steve Waterman
stevewaterman51
Apr 10, 2012 7:34 pm
1/2 octahedron edge 1 volume ... From: Alan M Date: 4/10/2012 3:24:44 PM To: antiprism@yahoogroups.com Subject: [antiprism] Re: quanta module tet ... 1.2 ???...
6804
Alan M
a.michelson
Apr 11, 2012 5:19 pm
Shape Volume (notes) Octa: 4 tet (dual of cube) Cube: 3 tet (dual of octa) 1/2 octahedron: 2 tet (square-based pyramid) Tetra: 1 tet (24 A mods)...
6805
Steve Waterman
stevewaterman51
Apr 11, 2012 5:43 pm
Alan, Nope. This is a gripe that I maintain re the Concentric Hierarchy... apples and oranges.... The cube of edge 1 is NOT as is suggested below... your chart...
6806
Alan M
a.michelson
Apr 11, 2012 8:19 pm
That's right — assuming that every edge length has a length of a (for apple): * According to http://en.wikipedia.org/wiki/Tetrahedron ...
6807
Michael Schievelbein
schievelbein
Apr 17, 2012 5:06 am
Thank you very much for your help. I must be really out of practice, because I cannot get you script to run. I saved the file in a writable directory and chmod...
6808
jhausman1
Apr 18, 2012 12:19 pm
It's possible that somebody has modeled this (in Antiprism?). I'd love it if someone here can tell me "browse here, dummy". I have this notion that, in the...
6809
Roger Kaufman
vortexswirling
Apr 18, 2012 6:28 pm
Hi Jim, Adrian is away for a few days, and I don't know the specific answer to your question. I do know that Adrian has model numerous jitterbugs at the pages...
6810
jhausman1
Apr 18, 2012 7:17 pm
Thanks, Roger. I'll take a look at these. Yes, I mean the Archimedean "truncated icosidodecahedron" -- I'm addressing only convex forms. - Jim...
6811
Alan M
a.michelson
Apr 19, 2012 5:31 pm
... oranges. "and it does not matter what size you assign to the edge since size is after all IRRELEVANT ...
6812
Steve Waterman
stevewaterman51
Apr 19, 2012 5:59 pm
Alan, "A regular tetrahedron is always one third volume of a cube, if and only if
the tetrahedron is inscribed in the cube!" Although this volume relationship...
6813
Alan M
a.michelson
Apr 19, 2012 8:09 pm
Definition of MENSURATION <http://www.merriam-webster.com/dictionary/mensuration> 1. the act of measuring : measurement ...
6814
Steve
stevewaterman51
Apr 19, 2012 9:00 pm
Allan, writes... ... Although this volume relationship of 1 to 3 is true...again, since the tet edge and cube edge are not the same length as one another, then...
6815
John Brawley
voodoo1776
Apr 19, 2012 9:13 pm
Mildy disagree: That three and only three tets of volume 'x' fit into one cube IFF one of them inscribes therein (as the inscription is done), does amount to a...
6816
Adrian Rossiter
adrianrossiter
Apr 20, 2012 9:28 am
Hi Michael ... The script is a Python script rather than a shell script, but is correctly being run as a Python script because of the first line of the script....
6817
Adrian Rossiter
adrianrossiter
Apr 20, 2012 11:35 am
Hi Jim ... I haven't modelled any jitterbug-like collapse of this shape. Have you sketched out the initial part of the transformation you have in mind, i.e the...
6818
jhausman1
Apr 20, 2012 11:58 am
Adrian - I'll start writing a comprehensive description. Meanwhile, here's a Wolfram Demonstration as one link in the continuum. ...
6819
jhausman1
Apr 20, 2012 12:19 pm
The steps that are problematic for me are trunc.icosidodeca to rhombicosidodeca, and trunc.cubocta to rhombicubocta. For the steps...
6820
jhausman1
Apr 20, 2012 12:23 pm
A suggestive image for the rhombicubocta-to-cubocta step: http://geomag.wikia.com/wiki/Truncated_Cuboctahedron_of_Cubes - Jim...
6821
jhausman1
Apr 20, 2012 12:27 pm
oops, that should have read "for the trunc.cubocta-to-rhombicubocta step"...
6822
jhausman1
Apr 20, 2012 12:45 pm
Here's how a dodecahedron can collapse to a tet.oct.tet: - Grasp two opposite dodeca vertices. Pinch the three edges to become one edge, thereby bringing that...
6823
Adrian Rossiter
adrianrossiter
Apr 20, 2012 1:40 pm
Hi Jim ... I think this would work to transform the truncated icosidodecahedron to an icosidodecahedron http://www.antiprism.com/misc/tr_icosid_to_icosid.jpg ...
6824
jhausman1
Apr 20, 2012 2:02 pm
I'm thinking of doing this with physical parts. Would this still work, if edges must continue to exist without disconnecting from their original vertices? I'm...
6825
Adrian Rossiter
adrianrossiter
Apr 20, 2012 2:19 pm
Hi Jim ... I don't believe there are any problems for the vertices to remain connected. The main problem for a physical model is probably the vertices crossing...
6826
Alan M
a.michelson
Apr 20, 2012 5:35 pm
... <http://en.wikipedia.org/wiki/If_and_only_if> all the edge lengths being compared are of a constant length (Wiki and MathWorld assume edge lengths of a),...
6827
John Brawley
voodoo1776
Apr 20, 2012 7:47 pm
Must "mensuration" be limited to equal-edge lengths when comparing _volumes_? That is, if one is comparing _lengths_ then the "mensuration" involved is ...
6828
Alan M
a.michelson
Apr 20, 2012 10:59 pm
Not all polyhedra <http://en.wikipedia.org/wiki/File:Cube_truncation_sequence.svg> have edges of the same length. ... is ... (by, say, ... this is ... or ... ...
6829
John Brawley
voodoo1776
Apr 20, 2012 11:06 pm
Not the point. Any polyhedron can be assigned an edge length, even of it's only one edge therein. --JBw ... From: "Alan M" <amichelson2002@...> To:...
