Talk:Truncated triakis tetrahedron
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In the one-with-regular-hexagons section, it would be nice if the dimensions of the pentagons were given. Just how far are those pentagons from being regular? Curiously, RobertAustin 14:11, 30 December 2006 (UTC)
- Hi Robert. Best I can suggest is to get the model and measure edge lengths: t6dtT. If done well, four edges can be equal and one edge must be long.) Tom Ruen 23:09, 30 December 2006 (UTC)
Triakis truncated tetrahedron[edit]
I think it relevant to point out the possibility of confusion between the truncated triakis tetrahedron and the triakis truncated tetrahedron which is a truncated tetrahedron ( cut offs one third of edge length ) which have the raised triakis treatment ( flattish tetrahedrons one quarter of the height of the cutoffs replacing them). These have been called by an author snub tetrahedrons which are something else. 217.207.112.194 22:38, 22 January 2007 (UTC)Robert Reid
- Agreed. Conway talks about the Triakis truncated tetrahedron, here. It is important because it is the shape of the Voronoi cells of the carbon atoms in diamond. It fill space, as shown here: 12. Approximately specified as k3tT (but with the kis'd vertices raised to the centroids of the mini tetrahedra that were snipped off). Any reason it shouldn't have its own page? Ferkel (talk) 14:37, 13 September 2012 (UTC)
feedback on Johnson near miss solid[edit]
I have been exploring the 'opposite of a football' recently. i.e. instead of pentagons surrounded by hexagons I wondered if you could have a solid where hexagons were surrounded by pentagons and this led me to the near-miss johnson solid. In my basic module I made the solid from regular polygons but of course there is some distortion - however because I left the hexagons as 'holes' there was no distortion but instead I had a non-planar hexagon. This has links with the chemists carbon rings. My hexagon hole appears to be what a chemist would call a 'puckered' hexagon in the configuration of 'the chair'. The entry on this solid does state that it is a'non-planar' hexagon with alternate angles of 108 and 132. But I think these angles are consistent with a planar hexagon. I get the angles to be 108 and 130.4 The maths behind this is detailed on my flickr website. Search for 'the yes man' and 'pentagon thingammy'. The chemists seem to have done a lot of work on this already and I thought a mention should be made of their work on 'puckered' carbon rings leading to analogies between these solids and 'cyclohexane' - this johnson solid or 'benzene' which has a planar 'hexagon'. Also to get a planar hexagon but keeping ALL edge lengths equal I calculated the pentagons would have angles of 115.726, 101.847, 110.290, 110.290, 101.847 (Angle sum 540) retaining 1 line of symmetry. The resultant planar hexagon would have alternating angles of 133.830 and 106.170 (a pairwise sum of 240). This hexagon although equilateral is obviously not regular so it is different to the example quoted above. (truncated triakis tetrahedron or ensuing topologically eqivalent Johnson solid) http://www.flickr.com/photos/the_yes_man/8086089135/in/photostream You will also find here some extended models using the near-miss Johnson solid as a 'building block.' This structure has obvious links with buckyballs and fullerenes (although I can't find it listed as a C28 fullerene anywhere although this structure does seem to exist as a 'puckered hexagon ring in the chair formation' as above in 'cyclohexane'. If the hexagons are left as holes then the shape suffers no distorton but carries a 'puckered hexagon ring' similar to cyclohexane. Further, these modules can be incorporated into a lattice, again with no distortion that means it could act as an efficient filter or sieve, with its regularity and large surface area akin to 'zeolite' found in washing powder. http://www.flickr.com/photos/the_yes_man/8297700177/in/photostream This is the first time I've been on Wikipedia so I don't know if I'm being helpful or not. What do you think? Tommybobbles (talk) 03:24, 3 December 2012 (UTC) 2nd December 2012--Tommybobbles (talk) 03:24, 3 December 2012 (UTC)