--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en
---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
Hello Mike,
Given the chord factors you mentioned -- for 6v icosa, class I, method 1 -- only the pentagons (BBBBB) and central hexagons (HHHHHH) are planar. The remaining "hexagons" (BDFHFD and FHFFHF) are not planar.
Here's an alternative set of chord factors that will give you a level-base hemispheric dome, all of whose hex and pent faces are planar (a true polyhedron). It's the geometric dual of a 4v icosa, class II geosphere. So, not all vertices lie exactly on the surface of the surrounding sphere; there are 3 slightly different radii.
B = 0.1964544
E = 0.1797097
F = 0.2015725
H = 0.2008482
I = 0.2228530
J = 0.4238917 (long struts along dome base)
Hope this helps.
- Gerry in Québec
Hi again Mike,
A few minutes ago I posted chord factors for your second hex-pent pic -- then realized I had used the wrong reference radius. So I deleted that post. The revised jpg, attached, gives the chord lengths when the surrounding sphere's radius is 1 unit.
Good luck with your models.
- Gerry
Hi Hector, thanks for the chord factors and pic, are all the faces planar ? to bad the base isnt flat :(I will have to read a book on the diferent methods used, cause i still dont understand why anyone would use the Mexican method when the method 1 is much easier and makes a flat base.
On Jan 22, 2016, at 22:08, mike wazowski <docuin...@gmail.com> wrote:
Hi Hector, thanks for the chord factors and pic, are all the faces planar ? to bad the base isnt flat :(I will have to read a book on the diferent methods used, cause i still dont understand why anyone would use the Mexican method when the method 1 is much easier and makes a flat base.
Hi Gerry,
Thanks Ken, i didnt know that.
--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en
---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
<Dual-of-4v-icosa-classI-hemi.png>
WOW Gerry that looks great !
I would really love to make a decent GP (2,2) so that i can move on to the next faze, GP (3,3) , which is the best looking one imo.
Hi Gerry,
Hi everyone,I was trying to make a paper model of a hex dome from a 6v class 1 geodesic dome.I used these measurements :B 0.1904769E 0.1873834F 0.1980126H 0.2153537I think the faces should be planar but on the actual paper model i coudnt align them.Any ideas what i did wrong ?Taff do you have the measuremets for a class II hex dome like the second pic ? (maybe with a level base ?)
Hi Mike,
I don't have a set of numbers for an I {3,3} Goldberg polyhedron that has a naturally flat base at a useful truncation when the zenith is a pentagon. As you can see in the attached diagram, this configuration, unlike the I {2,2}, doesn't split naturally into hemispheres. The imaginary equator runs between two edge pathways (red dashed lines). And, for this particular I {3,3} generated by Antiprism, those pathways zig-zag (green dashed lines).
As with the I {2,2}, there may exist an I {3,3} solution that gives you both planar hex faces AND a natural, clean truncation somewhere around the equator (e.g., 12/27, 13/27, 14/27, 15/27). However, I haven't done that exercise (it would be quite time consuming using my current tools).
One option is to make a 13/27 or a 15/27 dome, but move the base vertices into alignment to give a flat base (blue dashed lines). This involves some trig calculations and will add several edge lengths, which means you'd have several more face shapes to contend with. A second, much easier option is to follow Ken Brown's earlier suggestion and set the midpoint between pentagons as your dome zenith. Then you can split some hexes and pentagons down the middle to get an exact hemisphere with a flat base (second jpg attached).
Let me know what you think and we can take it from there.
- Gerry in Québec
How did your second run with I {2,2} turn out?
- Gerry
39-38-45 = 10-9-14 | |
38-45-52 = 9-10-15 | |
45-52-53 = 10-15-19 Cheers, - Gerry |
Hi Gerry and All
Here are two more 3D models:
4v icosa double-frame dome, 7/12 truncation, built as a 50-ft home in Vermont in 2013:
Icosa cap, 5 triangular frames using Oregon Dome's construction method (beveling the wide faces of 2x4s):
Any feedback on how easy or hard it is to view, manipulate and/or download such models would be welcome.
* * *
Adrian,
- Gerry
This polyhedron is similar to the outer grid of one of the Eden Project domes in Cornwall, UK. It was created using Antiprism’s pol_recip program (www.antiprism.com) which generates the duals of polyhedra. The starting point was a class II, 6v icosahedral geodesic sphere. Once the dual was created, it was truncated above the equator with the help of Excel. If you think of this polyhedron as representing a slice of Earth, then Costa Rica’s capital, San José, would lie a tad north of the truncation plane.
Hi Gerry