Moebius Edge Gallery

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moebius_edge_1-0+diag.jpg

A (2,1) torus knot bifilar electroform. copyright 2010 DEM


Bifilar halves in red and blue of torus knot groups

Web folder: http://groupkos.com/science2/products/torus_knot_bifilar/

The Bifilar Moebius Edge Gallery is named uniformly, expanding from a (1,0) unknotted circle through a (7,6) knot.

Additional files will be added in the future, such as this cutaway view following, and eventually more animation and/or video composed for various dynamic perspectives and such.

DonEMitchell 17:34, 26 September 2010 (MDT)


Fine print: Anyone may re-post these images which are my copyright, or derivatives you make, so long as attribution is preserved and they are not used in defamation --and only for non-commercial intent, educational or otherwise. I would appreciate a notice of use so I have some bragging-points with my supportive wife. I am bandwidth unlimited and It is OK to hotlink to these files to save yourself the transport, but there is no guarantee of continued access or location at the same URL. No animals have been harmed in this production.



(2,X) Torus Knots

2,1 Torus Knot

Bifilar 1/2 twist Moebius Edge as (2,1) torus knot
moebius_edge_2-1+y.jpg moebius_edge_2-1+x.jpg moebius_edge_2-1+z.jpg moebius_edge_2-1+diag.jpg
moebius_edge_2-1-y.jpg moebius_edge_2-1-x.jpg moebius_edge_2-1-z.jpg moebius_edge_2-1-diag.jpg


(3,X) Torus Knots

(3,1) Torus Knot

moebius_edge_3-1-z.jpg      


(3,2) Torus Knot

moebius_edge_3-2+y.jpg moebius_edge_3-2+x.jpg moebius_edge_3-2+z.jpg moebius_edge_3-2+diag.jpg
moebius_edge_3-2-y.jpg moebius_edge_3-2-x.jpg moebius_edge_3-2-z.jpg moebius_edge_3-2-diag.jpg


(4,X) Torus Knots

(4,1) Torus Knot

moebius_edge_4-1+y.jpg moebius_edge_4-1+x.jpg moebius_edge_4-1+z.jpg moebius_edge_4-1+diag.jpg
moebius_edge_4-1-y.jpg moebius_edge_4-1-x.jpg moebius_edge_4-1-z.jpg moebius_edge_4-1-diag.jpg


(4,2) Torus Knot

  • See (2,1)


(4,3) Torus Knot

moebius_edge_4-3+y.jpg moebius_edge_4-3+x.jpg moebius_edge_4-3+z.jpg moebius_edge_4-3+diag.jpg
moebius_edge_4-3-y.jpg moebius_edge_4-3-x.jpg moebius_edge_4-3-z.jpg moebius_edge_4-3-diag.jpg


(5,X) Torus Knots

(5,1) Torus Knot

moebius_edge_5-1+y.jpg moebius_edge_5-1+x.jpg moebius_edge_5-1+z.jpg moebius_edge_5-1+diag.jpg
moebius_edge_5-1-y.jpg moebius_edge_5-1-x.jpg moebius_edge_5-1-z.jpg moebius_edge_5-1-diag.jpg


(5,2) Torus Knot

moebius_edge_5-2+y.jpg moebius_edge_5-2+x.jpg moebius_edge_5-2+z.jpg moebius_edge_5-2+diag.jpg
moebius_edge_5-2-y.jpg moebius_edge_5-2-x.jpg moebius_edge_5-2-z.jpg moebius_edge_5-2-diag.jpg


(5,3) Torus Knot

moebius_edge_5-3+y.jpg moebius_edge_5-3+x.jpg moebius_edge_5-3+z.jpg moebius_edge_5-3+diag.jpg
moebius_edge_5-3-y.jpg moebius_edge_5-3-x.jpg moebius_edge_5-3-z.jpg moebius_edge_5-3-diag.jpg


(5,4) Torus Knot

moebius_edge_5-4+y.jpg moebius_edge_5-4+x.jpg moebius_edge_5-4+z.jpg moebius_edge_5-4+diag.jpg
moebius_edge_5-4-y.jpg moebius_edge_5-4-x.jpg moebius_edge_5-4-z.jpg moebius_edge_5-4-diag.jpg


(6,X) Torus Knots

(6,1) Torus Knot

moebius_edge_6-1+y.jpg moebius_edge_6-1+x.jpg moebius_edge_6-1+z.jpg moebius_edge_6-1+diag.jpg
moebius_edge_6-1-y.jpg moebius_edge_6-1-x.jpg moebius_edge_6-1-z.jpg moebius_edge_6-1-diag.jpg


(6,2) Torus Knot

  • See (3,1)


(6,3) Torus Knot

  • See (2,1)


(6,4) Torus Knot

  • See (3,2)


(6,5) Torus Knot

moebius_edge_6-5+y.jpg moebius_edge_6-5+x.jpg moebius_edge_6-5+z.jpg moebius_edge_6-5+diag.jpg
moebius_edge_6-5-y.jpg moebius_edge_6-5-x.jpg moebius_edge_6-5-z.jpg moebius_edge_6-5-diag.jpg


(7,X) Torus Knots

(7,1) Torus Knot

moebius_edge_7-1+y.jpg moebius_edge_7-1+x.jpg moebius_edge_7-1+z.jpg moebius_edge_7-1+diag.jpg
moebius_edge_7-1-y.jpg moebius_edge_7-1-x.jpg moebius_edge_7-1-z.jpg moebius_edge_7-1-diag.jpg


(7,2) Torus Knot

moebius_edge_7-2+y.jpg moebius_edge_7-2+x.jpg moebius_edge_7-2+z.jpg moebius_edge_7-2+diag.jpg
moebius_edge_7-2-y.jpg moebius_edge_7-2-x.jpg moebius_edge_7-2-z.jpg moebius_edge_7-2-diag.jpg


(7,3) Torus Knot

moebius_edge_7-3+y.jpg moebius_edge_7-3+x.jpg moebius_edge_7-3+z.jpg moebius_edge_7-3+diag.jpg
moebius_edge_7-3-y.jpg moebius_edge_7-3-x.jpg moebius_edge_7-3-z.jpg moebius_edge_7-3-diag.jpg


(7,4) Torus Knot

moebius_edge_7-4+y.jpg moebius_edge_7-4+x.jpg moebius_edge_7-4+z.jpg moebius_edge_7-4+diag.jpg
moebius_edge_7-4-y.jpg moebius_edge_7-4-x.jpg moebius_edge_7-4-z.jpg moebius_edge_7-4-diag.jpg


(7,5) Torus Knot

moebius_edge_7-5+y.jpg moebius_edge_7-5+x.jpg moebius_edge_7-5+z.jpg moebius_edge_7-5+diag.jpg
moebius_edge_7-5-y.jpg moebius_edge_7-5-x.jpg moebius_edge_7-5-z.jpg moebius_edge_7-5-diag.jpg


(7,6) Torus Knot

moebius_edge_7-6+y.jpg moebius_edge_7-6+x.jpg moebius_edge_7-6+z.jpg moebius_edge_7-6+diag.jpg
moebius_edge_7-6-y.jpg moebius_edge_7-6-x.jpg moebius_edge_7-6-z.jpg moebius_edge_7-6-diag.jpg


Torus cross-section patterns

Notice the square pattern in the cross-section of the (4,3) knot below:

moebius_edge_4-3_bifilar_cutaway_512x384.jpg

The 3-class knots have a triangular cross-section pattern, the 5-class a pentagonal pattern, etc.

Note that in the animation sequence above, the same rendering is used in each frame, only rotated incrementally through the cutaway about the axis through the torus center, creating a nice illusion of toroidal rotation because a cutaway view doesn't afford view of the whole object rotating. However, the same toroidal rotational dynamic is afforded by phase stepping a 3-phase coil set.


Polyphase

Moebius edge 002 x 512x384.png

tk21_3ph_moebius_bifilar.gif

torus_spinwave_moebius_cross-field_1920x1080.jpg