Hi Adrian, What is the calculation for the height of a snub antiprism? I suppose it depends on the value of -s n. The polygons of the snub antiprisms could be...
1397
Adrian Rossiter
adrianrossiter
Feb 3, 2008 3:23 pm
Hi Roger ... Yes, n depends on the ring radius, and this with the polygon determines the height. I have included the code I use below. It shows how the height...
1398
hedron
Feb 3, 2008 8:08 pm
Adrian Hi. The concept of having a "nearness rating" that is dependent on the number of edges has come up previously on the poly list, although I must say that...
1399
Adrian Rossiter
adrianrossiter
Feb 4, 2008 10:19 am
Hi Jim ... I had in mind that the relationship would go the other way, and that having more faces/edges would lower the value of the rating. In which case the...
1400
vortexswirling
Feb 5, 2008 2:40 am
Hi Adrian, You may have see this. http://spidron.hu/archispidron/ The spidron utility doesn't seem to work like this, though. Often it won't do the...
1401
Adrian Rossiter
adrianrossiter
Feb 5, 2008 11:49 am
Hi Roger ... The program won't make these. They appear to made from two spidron modules per edge, whereas the normal construction only has one module per edge ...
1402
Adrian Rossiter
adrianrossiter
Feb 5, 2008 12:02 pm
Hi Roger ... I forgot this bit. There is a limited range of angles that will make the spidron units close for a particular polygon. You can see this by running...
1403
vortexswirling
Feb 5, 2008 2:57 pm
Hi Adrian, I've looked at the ratio of star antiprisms to their retrograde pair. I'm looking at snub antiprisms now. There are some problems compiling. I have...
1404
Adrian Rossiter
adrianrossiter
Feb 5, 2008 4:17 pm
Hi Roger ... The third argument is for the complex parts of complex roots. If you don't want those then you can pass 0 for the third argument (0 is given as a...
1405
vortexswirling
Feb 5, 2008 8:09 pm
Hi Adrian, I had guess that "type" was the -s parameter so was able to make some headway. ... Over lunch I left it run up to 30000 (only coprime n/d) and never...
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Adrian Rossiter
adrianrossiter
Feb 6, 2008 11:04 am
Hi Roger ... It didn't really have more than two values in the end. Plugging a root into the height equations produced a valid intermediate height value of 0....
1407
Adrian Rossiter
adrianrossiter
Feb 6, 2008 4:12 pm
... and 9 -s 0 and 2 -s 1. I think that is all of them. Adrian. -- Adrian Rossiter adrian@... Home: http://antiprism.com/adrian...
1408
hedron
Feb 7, 2008 10:59 am
Adrian I have been trying for some time to generate the full set of Isohedral Deltahedra as set out in Shepherd's paper of the same name, published in 1999....
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Adrian Rossiter
adrianrossiter
Feb 7, 2008 12:30 pm
Hi Jim ... I think I get that. These are Schwartz triangles. It looks like these can be obtained from the kaleido code (that Antiprism includes). Have a look...
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Adrian Rossiter
adrianrossiter
Feb 7, 2008 12:39 pm
... Schwarz triangles. Adrian. -- Adrian Rossiter adrian@... Home: http://antiprism.com/adrian...
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vortexswirling
Feb 7, 2008 3:50 pm
Hi All, All the proper n/d snub antiprisms have all vertices with connectivity 5 with only one exception. The case of n = 2. For n = 2 (-s 0 and 1) there are 4...
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Adrian Rossiter
adrianrossiter
Feb 8, 2008 9:58 am
Hi Roger ... It shows the sensitivity to the fraction change around the largest possible fraction. The damping effect as the sequence progresses also suggests...
1413
vortexswirling
Feb 12, 2008 5:07 pm
Hi Adrian, Did you try anything with Shephards method? I thought it might be fun to add dipyramids to the program using Shephards formulas and then rotating...
1414
Adrian Rossiter
adrianrossiter
Feb 13, 2008 12:48 pm
Hi Roger ... I have made some progress on the search program. For a symmetry type you pass three vectors. These corrspond to rotation axes through a face,...
1415
vortexswirling
Feb 13, 2008 3:45 pm
Hi Adrian, ... It sounds like you are having luck. I tried some more with the dipyramid formula with no luck. It seems to me that if one is trying to make a...
1416
hedron
Feb 13, 2008 4:08 pm
Hi Roger and Adrian Your approach looks good to me. I can't wait to see the icosahedral results. Given that Shephard's paper missed 5 solutions ( I can only ...
1417
Adrian Rossiter
adrianrossiter
Feb 14, 2008 9:22 am
Hi Jim ... There seem to be some numeric issues to my approach. What I am finding is that when I use A, B, C to calculate b and c then I check distances and...
1418
Adrian Rossiter
adrianrossiter
Feb 14, 2008 11:19 am
Hi Roger ... It looks like alpha should be the reciprocal of what is given i.e. 1/(2*sin(PI*d/n)). Adrian. -- Adrian Rossiter adrian@... Home:...
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vortexswirling
Feb 14, 2008 12:53 pm
Hi Adrain, ... I should have tried this as I was trying everything else! A hint was that for gamma, sqrt(1 - (term*term)) didn't specify absolute value, so ...
1420
Adrian Rossiter
adrianrossiter
Feb 14, 2008 1:09 pm
Hi Roger ... You will have to turn 90 degrees around the x-axis, and may need to follow that by a 90 degree turn around the y-axis. ... You can use polygon -E...
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vortexswirling
Feb 14, 2008 6:55 pm
Hi Adrian, ... This worked. For even n only the x-axis rotation was needed, but for odd n, with the y-axis rotation, the results were a compound of two n/d ...
1422
vortexswirling
Feb 14, 2008 9:32 pm
... This would be the compound of 5 octahedra. The octahedra can be thought of the 4/1 dipyramid. Then the compound is easily made as polygon -t dip 4 |...
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Adrian Rossiter
adrianrossiter
Feb 15, 2008 6:51 pm
Hi Roger and Jim ... I have run the seach program and started looking through the output. For the octahedral cases it missed the compound of 3 octahedra. At...
1424
vortexswirling
Feb 15, 2008 8:39 pm
Adrian, ... reflection ... Another way to look at this is that 8-fold dihedral symmetry of the 8/3 dipyramid can fit inside the reflection planes of octahedral...
1425
vortexswirling
Feb 16, 2008 2:54 am
Hi, ... Actully this happens if a cut is made anywhere between the reflection planes. Here is a model of a cube that has been cut this way and the halves...
