Semi-regular conical knots

Cone geodesics Geodesics on a cone are easily found using the fact that the surface is isometric to the plane. http://demonstrations.wolfram.com/ConeGeodesics/

Projection cone geodesics

Description conical knot

(B)ights= 10, (L)eads= 4, (R)hythm: step1= 3 , step2= 5

Possible conical knots for bights < 22 Rhythm 3,5 B2L4R3,5 ; B6L4R3,5 ; B10L4R3,5 ; B14L4R3,5 ; B18L4R3,5 ; B22L4R3,5 ; Rhytm 3,7 B2L5R3,7 ; B4L5R3,7 ;B6L4R3,7 ;B8L5R3,7 ;B12L5R3,7 ;B14L5R3,7; B16L5R3,7 ;B18L5R3,7 ; B22L5R3,7 ; Rhythm 3,9 B2L6R3,9 ;B10L6R3,9 ;B14L6R3,9 ;B22L6R3,9 ; Rhythm 5,7 B2L6R5,7 ; B10L6R5,7 ;B14L6R5,7 ;B22L6R5,7 ; Rhythm 5,9 B2L7R5,9 ;B4L7R5,9 ;B6L7R5,9 ;B8L7R5,9 ;B10L7R5,9 ;B12L7R5,9; B16L7R5,9 ;B18L7R5,9 ;B20L7R5,9 ;B22L7R5,9 ; Rhythm 7,9 B2L6R7,9 ; B6L6R7,9 ;B10L6R7,9 ;B14L6R7,9 ;B18L6R7,9 ;B22L6R7,9 ;

Isometric graph-paper

Principle:

Isometric graph-paper bights > Conical knot [2*max (step1,step2)]

Rhythm 3,5

Rhythm 3,7

Rhythm 3,9

Rhythm 5,7

Rhytm 5,9

Rhythm 7,9

Example

B2L4R3,5

B6L4R3,5

B10L4R3,5

B14L4R3,4

B12L5R3,7

Application 1. Hanging flowerpot (stable geodesic lines) ,

2. Support.

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by Struktor 2013