CUBES WOVEN ON THE SKEW

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Bridges 2007 – Summary

The results are given below in the form of two tables and a photograph. Copies of summary table 1 and summary table 2 (plus photo) are also available in Adobe Acrobat format.

Summary table 1 for cubes 0,1 to 5,5

(key below table)

There is no need to construct any further cubes in this series as predictable.

In the table above, groups of cubes with the same characteristics are marked in colours:

Category 1 [lemon] where b or c = 0,
Category 2 [purple] where b = c,
Category 3A [pale blue] where b and c are prime numbers or 1,
Category 3B [orange] where b + c = prime number.

Other groups are yet to be investigated.

b and c: see paper for explanation
W = wind number: the number of times the loop, following the path of one weaving element, goes around the cube
N = number of loops to cover
T = twist number: the number of twists in this loop when removed from the cube. The significance of values of T is still under investigation.
L = length of loop in centimetres. The above measurements were made when cubes drawn on 1cm grid thus = number of squares.

Faces of the cube are numbered as on a die – thus 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.

See also Labelling the faces of a cube (.pdf).

Summary table 2 for cubes 0,1 to 5,5

 

Photograph of cubes 0,1 to 5,5