“7₄ knot”的意思、由来-开放百科全书

词条

7₄ knot

释义

Visual representations
Example
Sources

{{Infobox knot theory
| name= 7₄
| practical name=
| image= Blue 7 4 Knot.png
| caption=
| arf invariant= 0
| braid length= 9
| braid number= 4
| bridge number= 2
| crosscap number= 3
| crossing number= 7
| genus= 1
| hyperbolic volume= 5.13794
| linking number=
| stick number= 9
| unknotting number= 2
| conway_notation= [313]
| ab_notation= 7₄
| dowker notation= 6, 10, 12, 14, 4, 2, 8
| thistlethwaite=
| last crossing= 7
| last order= 3
| next crossing= 7
| next order= 5
| alternating= alternating
| class= hyperbolic
| fibered=
| pretzel=
| prime= prime
| slice=
| symmetry= reversible
| tricolorable= tricolorable
}}

In mathematical knot theory, 7₄ is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism and/or artistic ornamentation of various cultures. This knot has 14 intersections with 7 crossing-over.

Visual representations

The interlaced version of the simplest form of the Endless knot symbol of Buddhism is topologically equivalent to the 7₄ knot (though it appears to have nine crossings), as is the interlaced version of the unicursal hexagram of occultism.^[1] (However, the endless knot symbol has more complex forms not equivalent to 7₄, and both the endless knot and unicursal hexagram can appear in non-interlaced versions, in which case they are not knots at all.)

Example

Sources

1. ^{{Knot Atlas|7_4}}
2. ^Celtic Art: The Methods of Construction by George Bain, p. 27 ({{ISBN|0-486-22923-8}})

1 : Double torus knots

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