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Pete Richards
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Location: Northeast Ohio
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Posted: Oct 25, 2012 16:04 Post subject: Re: About cyclic twinning - (5) |
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A correction: the marcasite cyclic twin (on the previous page) is from Cedarville, Ohio, not Cedarville, Iowa!
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Ru Smith
Joined: 13 Oct 2012
Posts: 362
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Posted: Oct 25, 2012 18:14 Post subject: Re: About cyclic twinning - (5) |
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Fabulous pictures!
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Jordi Fabre
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Posted: Oct 25, 2012 23:20 Post subject: Re: About cyclic twinning - (5) |
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Pete Richards wrote: | A correction: the marcasite cyclic twin (on the previous page) is from Cedarville, Ohio, not Cedarville, Iowa! |
Fixed
Thank you to everybody for this thread. Great discussion!
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Ru Smith
Joined: 13 Oct 2012
Posts: 362
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Posted: Oct 26, 2012 18:49 Post subject: Re: About cyclic twinning - (5) |
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Cassiterite is often seen in geniculate twins, but sometimes there are very interesting cyclics. Here are three examples, from Cornwall, Australia and Bohemia.
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Cassiterite, tetragonal dipyramids in 6 member cyclic twin Cornwall 15 mm |
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Cassiterite, cyclic twin of three geniculates Copes Creek, Tingha Tinfield, Hardinge County, New South Wales, Australia 2 cm |
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Cassiterite, 3 member cyclic twin Horni Slavkov (Schlaggenwald), Karlovy Vary, Bohemia, Czech Republic. 15 mm |
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Peter Farquhar
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Posted: Nov 11, 2012 15:03 Post subject: Re: About cyclic twinning - (5) |
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Magic with cyclic twinning
As a magician, I enjoy all forms of illusions – both man-made and natural. Magicians often create illusions for their audience members by forcing them to adopt a particular perspective, whether they realize it or not. Later the magician might change this initial perspective (using a variety of subtle maneuvers) to surprise and delight the audience. Cyclic twins can also reveal big surprises when looked at from multiple perspectives, or different points of view.
The famous mathematician H. M. S. Coxeter was one of the early crystallographers to demonstrate the key role of multiple perspectives in understanding crystal structure and symmetry. Coxeter was also an amateur magician and inspired many of the visual illusions by the Dutch artist M. C. Escher. One of my favorite illustrations is Escher’s 1953 lithograph, “Relativity,” (for copyright purposes, please see the image on the official website at https://www.mcescher.com/Shopmain/ShopEU/facsprints-uk/prints.html In a moment, I’ll suggest an analogy between this Escher drawing and a cyclic twinned rutile.
Escher’s “Relativity” combines three alternate perspectives in one architectural structure where the normal laws of gravity apparently do not apply. In viewing this drawing for the first time, most individuals implicitly adopt one perspective of “up and down.” In rotating the drawing (or otherwise changing their perspective), individuals are then surprised to discover other valid perspectives exist, which may either better explain what they see or add to the contradictions experienced (see Scott McDaniel’s excellent analysis of this artwork at https://www.scottmcd.net/artanalysis/?p=548
(links normalized by FMF)
We’ll now examine a rutile twin (PF-3306) from Natus Farm, near Gamsberg Mountain in the Khomas Region of Namibia.
CAUTION: Please look carefully at each 2-D image in the sequence without jumping ahead; at each step, imagine what the entire specimen looks like in 3-D. Try not to peek at the fifth and last image until the very end.
Please note the images are all of the same mineral specimen taken from five different points of view; the different perspectives (labeled north, west, south, east) in the first four images are generated by rotating the specimen a quarter turn from right to left each time; the last image shows a top-down view of the specimen.
Let us know what you see in this rutile specimen when viewed from multiple perspectives.
Peter Farquhar
Claremont, California
USA
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Rutile (PF-3306) Natus Farm, Gamsberg Mountain, Khomas Region, Namibia 3.0 x 2.4 x 2.1 cm Perspective #1 - north |
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Rutile (PF-3306) Natus Farm, Gamsberg Mountain, Khomas Region, Namibia 3.0 x 2.4 x 2.1 cm Perspective #2 - west |
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Rutile (PF-3306) Natus Farm, Gamsberg Mountain, Khomas Region, Namibia 3.0 x 2.4 x 2.1 cm Perspective #3 - south. |
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Rutile (PF-3306) Natus Farm, Gamsberg Mountain, Khomas Region, Namibia 3.0 x 2.4 x 2.1 cm Perspective #4 - east. |
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Rutile (PF-3306) Natus Farm, Gamsberg Mountain, Khomas Region, Namibia 3.0 x 2.4 x 2.1 cm Perspective #5 - top-down |
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Antonio Alcaide
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Posted: Nov 11, 2012 16:28 Post subject: Re: About cyclic twinning - (5) |
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Thank very much, Peter, for your reference to Coxeter and Escher, one of my favourite painters. Now I understand my double interest in Escher and crystallography. Your analogy between "Relativity" and a rutile twin is actually "food for thought".
Regards
_________________ Life is the shortest crystal |
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Ru Smith
Joined: 13 Oct 2012
Posts: 362
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Posted: Nov 12, 2012 21:17 Post subject: Re: About cyclic twinning - (5) |
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Very enjoyable post. Thank you!
This is what happens when you visit the Escher Museum in Den Haag (attached photo).
In your nice twin I see a "threeling" in one plane which took off into an "attempt" at a "sixling" in a perpendicular plane. The "sixling" shares the character of my "Kipushi"/"Kinyanfumbe" (if such a place actually exists) specimen in having parallel opposing sides (left-right in your image).
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Ru Smith
Joined: 13 Oct 2012
Posts: 362
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Posted: Nov 12, 2012 21:30 Post subject: Re: About cyclic twinning - (5) |
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By the way, M.C.'s half brother Berend George Escher was a mineralogy professor at Leiden University. He "had some influence on M.C.'s work due to his knowledge of crystallography."
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Peter Farquhar
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Joined: 14 May 2011
Posts: 51
Location: Virginia
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Posted: Nov 15, 2012 19:21 Post subject: Re: About cyclic twinning - (5) |
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Thanks to Ru Smith for the delightful photo from the Escher Museum. It seems the handsome children on the left side of the room are much taller than the folks on the right.
This so-called “Ames room illusion” can occur when a trapezoidal shaped room secretly replaces the familiar rectangular room. By controlling other perceptual cues, the Ames room seems normal, while more distant objects on the right appear smaller than closer objects of the same size positioned on the left.
For fun, mineral collectors might consider using the Ames illusion to change the sizes of their mineral specimens. For example, larger specimens could be made to appear the size of miniature or thumbnail specimens when positioned appropriately in an Ames (trapezoidal) case rather than in the conventional rectangular display case. Imagine if all your specimens could look exactly the same size! Of course, this innovation in display case construction technology might affect the rules for future competitions.
On the other hand, collectors might be more interested in making their mineral specimens appear larger than life. Like the Ames illusion, the principle of forced perspective could be applied to achieve the desired growth in specimen size.
For instance, the photo below shows a proud Pennsylvania farmer showing off the giant cyclic twinned rutile specimen he recovered when plowing his field near Parkesburg. (This farmer also reportedly grows huge, record-breaking pumpkins in the same fields; it must be the special fertilizer he uses.)
Enjoy.
Peter Farquhar
Claremont, California
USA
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Rutile sixling (PF-3277) Parkesburg, Sadsbury Township, Chester County, Pennsylvania, USA 5.5 x 5.5 x 5.0 cm A remarkably large, well formed rutile sixling from Parkesburg (photographed beside a small farmer). |
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Antonio Alcaide
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Posted: Nov 15, 2012 20:02 Post subject: Re: About cyclic twinning - (5) |
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Suggestive!!
My humble contribution to this approach to Escher universe. A link to the Parque de las Ciencias (Science Museum) exhibition in my city, Granada (Spain): M. C. Escher: Infinite Universes.
https://www.eschergranada.com/es/exposicion/ambitos
(link normalized by FMF)
Regards
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Pete Richards
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Joined: 29 Dec 2008
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Location: Northeast Ohio
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Posted: Nov 15, 2012 21:33 Post subject: Re: About cyclic twinning - (5) |
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Well, this thread is getting a bit chaotic as well as distorted (though fun). I will just add that all fishermen always hold their catch at arm's length from their body when a picture is being made. The fish appears huge, but so do the fingers holding it!
I will spare you a picture of my most recent catch!
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Peter Farquhar
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Posted: Nov 26, 2012 15:51 Post subject: Re: About cyclic twinning - (5) |
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Returning to the origins of this thread, I’d like to explore the criteria for a three-sided specimen to be a cyclic twin (i.e., a three-ling or trilling). I’m especially interested in triangular specimens – what we earlier called a “closed loop” – rather than partial sixlings with three sides completed (an "open loop"), or geniculated twins with three sides not forming a loop ("no loop").
For example, the rutile crystal on the specimen pictured below (PF-2123) has been described as “a rare contact twin of triangular aspect” (see the caption for figure 23 in Robert Cook’s article on “The Mineralogy of Graves Mountain, Lincoln County, Georgia” in the Mineralogical Record, volume 16, November-December 1985).
This article also mentions, “Graves Mountain rutile is morphologically complex. … Eightlings are common, as are sixlings. … Fourlings and trillings are less common.”
So here’s my question. What is the difference between a rutile twin of “triangular aspect” and a trilling?
Furthermore, I’m curious to see if anyone has closed-loop examples of trillings or fourlings to share on FMF?
Peter Farquhar
Claremont, California
USA
Description: |
Rutile (PF-2123) Graves Mountain, Lincoln County, Georgia USA 5.1 x 4.4 x 3.9 cm Rutile crystal on a matrix of iron oxide coated kyanite from Graves Mountain, Georgia. The main crystal is 1.9cm on each side of the equilateral triangle. |
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Pete Richards
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Posted: Nov 28, 2012 09:47 Post subject: Re: About cyclic twinning - (5) |
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The morphology of rutile from Graves Mountain is complex indeed! And untwinned crystals are definitely the exception. I'm not sure I understand the morphology of Peter's triangular crystal, so will refrain from an opinion about whether it is a trilling or not.
I have several twins from Graves Mountain which have a morphology vaguely like gypsum crystals. A number of years ago (1996, in fact) I spent quite a bit of time puzzling over them, and eventually figured them out, sort of. Amazingly, I still have the files and can still open them!
These crystals appear to basically be contact twins with one side much larger than the other. The main flat faces are composed of faces of {100} belonging to both individuals; these faces are co-planar (in theory) or nearly so (in reality).
Attached are several diagrams to try to show how these twins are put together. The first shows an ideal twin on {101} of a crystal of this habit. The next drawing shows the distortions that are seen on the actual twin - the left individual is greatly reduced and the prism is complete gone on the top. Note the characteristic deflection where the prism faces of the right individual meet the termination faces of the left individual. Some of the faces of the right crystal are greatly reduced or eliminated, leading to the "monoclinic" appearance.
But there's more. When you look at the end of the right-hand individual, there is a characteristic thin slice along the mid-line which does not quite fit the rest of the crystal. This can be interpreted as a little slice of the left-hand crystal, and in fact thin sections show a thin layer running the length of the crystal, though it often does not show at the surface except at the end. Thus there are only two individuals involved in this twin, and it combines aspects of contact and penetration twinning in a most novel way.
I believe this little misfit encourages rapid nucleation of new crystal growth, causing the distortion to "monoclinic" symmetry.
I also have examples of similar morphology from the Champion Mine, Mono County, California, again with the little wedge at the end of the elongated point.
This relates to Peter's triangular crystal in the following way. Both have major flat faces with a thin line visible parallel to one edge. This is the contact plane for the twin. I think a morphology like Peter's triangular crystal could be developed from my drawings by further selective distortion, but I do not know why it would happen. Perhaps Peter's crystal involves three individuals rather than two.
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Rutle (twin) Graves Mountain, Lincolnton County, Georgia, USA RPR Specimen #1342 Twin is 2 cm across |
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Sketches of rutile twin showing mode of distortion |
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The mysterious little sliver at the right end of the pointed crystal. |
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Peter Farquhar
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Posted: Dec 02, 2012 22:37 Post subject: Re: About cyclic twinning - (5) |
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Thanks to Pete Richards for his most recent post on twinning in Graves Mountain rutiles. I appreciate the time and skill needed to put together such an instructive discussion with great photos and diagrams.
In particular, Pete's last diagram on the “mysterious little sliver” hit home with me -- by illustrating the subtle difficulties in really understanding twinning. As a result, I’m reviewing a number of specimens in my collection to reconsider what twinning is actually occurring. As Pete mentioned earlier, it’s a long, twisted road.
For fun, the photo below shows another cyclic twinned rutile (PF-2655) from Graves Mountain, Georgia. From the side, the specimen has the familiar zig-zag profile of a rutile eightling (like the one (PF-2965) I posted earlier). The top-down view shown in the photo, however, reveals a much more complex twinning. I’ll pass for now on figuring this one out, but it's fun to try.
Meanwhile, please let me know if anyone has photos of closed-loop trillings or fourlings. I have seen a few and am very interested in seeing others.
Peter Farquhar
Claremont, California
USA
Description: |
Rutile cyclic twin (PF-2655) Graves Mountain, Lincoln County, Georgia, USA 2.5 x 2.3 x 2.2 cm. A complex 1.8 cm cyclic twin rutile crystal found on January 12, 1997 by Terry Ledford and Jean Tipton in the front quarry of Graves Mountain. (PF-2655) |
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Duncan Miller
Joined: 25 Apr 2009
Posts: 138
Location: South Africa
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Posted: Dec 03, 2012 11:34 Post subject: Re: About cyclic twinning - (5) |
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I have posted a photo of this specimen and its description along with an article about its locality before, but as I don't know how to link to another part of the forum, here is a repeat.
Illustration of the formation of a complex polycyclic twin in adularia feldspar. A: Diagram of an idealised monoclinic adularia single crystal viewed obliquely from the right, showing the narrow side pinacoid b, the broad prism faces m, the basal pinacoid c, and the second-order pinacoid x. B: Diagram of the adularia crystal viewed from the side, showing the crystallographic axes. The c-axis is vertical, the b-axis emerges perpendicularly from the page, while the a-axis is inclined by 116º to the vertical plane bearing the b and c-axes. The basal pinacoid c is parallel to the inclined a-axis, and the prism faces m and side pinacoid b are parallel to the vertical c-axis. C: Drawing of the adularia single crystal viewed obliquely from the right, showing the approximate trace of the {021} Baveno twin plane, as a thick line, on the crystal faces. The right hand portion of the crystal is mirror reflected through the twin plane to produce the pyramidal twin illustrated in D, viewed from above. Polycyclic twinning, involving four twin pairs like those in D, can be visualised as four-fold rotation of the Baveno twin around the shared a-axis, represented by the line joining the upper two c faces. This produces the complex cyclic twin sketched in E, viewed from above, from a real example found by Lesley Bust. The corner fishtail grooves can be on either the upper or lower surface, depending on the relative development of the basal pinacoid c and the second-order pinacoid x faces. This particular example also has some evidence of reflection twinning across the {100} plane, parallel to the vertical plane containing both the b and c-axes of the untwinned crystals, so three different twin laws are involved here.
Duncan
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Adularia Vredendal Limestone Quarry 10 cm across |
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Jordi Fabre
Overall coordinator of the Forum
Joined: 07 Aug 2006
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Location: Barcelona
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Peter Farquhar
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Joined: 14 May 2011
Posts: 51
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Posted: Dec 15, 2012 16:07 Post subject: Re: About cyclic twinning - (5) |
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I enjoyed Duncan’s recent photo of the complex twin of adularia, as well as his detailed analysis and enlightening diagrams that unlock this twinning puzzle. Very nicely done.
In turn, I want to share a rare (unaltered) photo illustrating cyclic twinning in humans. Best wishes for a magical holiday season from the five of us.
Peter
Description: |
Cyclic Twins Los Angeles, California USA Rare example of five-fold cyclic twinning in humans captured by John Gaughan at his magic shop in Los Angeles on November 7, 2009. |
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Pete Richards
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Location: Northeast Ohio
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Posted: Dec 15, 2012 16:33 Post subject: Re: About cyclic twinning - (5) |
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Most remarkable! The individuals of this complex twin are not even in contact with each other - a non-contact fiveling!
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Jordi Fabre
Overall coordinator of the Forum
Joined: 07 Aug 2006
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Posted: Dec 15, 2012 16:54 Post subject: Re: About cyclic twinning - (5) |
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Pete Richards wrote: | ...The individuals of this complex twin are not even in contact with each other.... |
Maybe better.... ;-) ;-)
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domenico
Joined: 31 Dec 2012
Posts: 28
Location: Garbagnate Mil.-Italy
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Posted: Dec 31, 2012 07:36 Post subject: Re: About cyclic twinning - (5) |
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My little contribution for this good topic...
Sorry for having only an old "diapositive" digitalyzed but the sample is not in my collection.
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Rutile Crevoladossola quarries, Ossola Valley-Italy 1 mm Photo B.Turconi Colleection P.Barili |
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