cinquefoil knot
type: Thing
alternate name: (5,2) torus knot
alternate name: 5_1
alternate name: 5₁
description: torus knot with crossing number 5
additional property: PropertyValue
  property ID: P18
  value: Blue Cinquefoil Knot.png
additional property: PropertyValue
  property ID: P31
  value: prime knot
additional property: PropertyValue
  property ID: P31
  value: torus knot
additional property: PropertyValue
  property ID: P31
  value: alternating knot
additional property: PropertyValue
  property ID: P373
  value: Cinquefoil knots
additional property: PropertyValue
  property ID: P646
  value: /m/0408kdl
additional property: PropertyValue
  property ID: P1889
  value: pentagram
additional property: PropertyValue
  property ID: P2812
  value: SolomonsSealKnot
additional property: PropertyValue
  property ID: P5350
  value: t^2 - t + 1 - t^{-1} + t^{-2}
additional property: PropertyValue
  property ID: P5351
  value: z^4 + 3z^2 + 1
additional property: PropertyValue
  property ID: P5352
  value: q^{-2} + q^{-4} - q^{-5} + q^{-6} - q^{-7}
additional property: PropertyValue
  property ID: P6104
  value: WikiProject Mathematics
additional property: PropertyValue
  property ID: P6366
  value: 2777055596
additional property: PropertyValue
  property ID: P6432
  value: 5_1
additional property: PropertyValue
  property ID: P8378
  value: 6, 8, 10, 2, 4
additional property: PropertyValue
  property ID: P8416
  value: 5a_{2}
additional property: PropertyValue
  property ID: P8426
  value: 5_1
additional property: PropertyValue
  property ID: P8427
  value: 5_1
additional property: PropertyValue
  property ID: P11034
  value: \{-1, 2, -3, 4, -5, 1, -2, 3, -4, 5\}
additional property: PropertyValue
  property ID: P11035
  value: +5
confidence:
  popularity graph score:
    score: 0.005
    score pct: 0
    tier: long_tail
    components:
      sitelinks: 6
      sitelinks norm: 0.014
      unique citations: 0
      unique citations norm: 0.0
      monthly pageviews: 98
      monthly pageviews norm: 0.0
  sitelinks: 6
  unique citations: 0
  monthly pageviews: 98
  yearly pageviews: 239
  pageview trend:
    m: 2026-08
    v: 98
  pageview trend:
    m: 2026-07
    v: 37
  pageview trend:
    m: 2026-06
    v: 33
  pageview trend:
    m: 2026-05
    v: 19
  pageview trend:
    m: 2026-04
    v: 51
  pageview trend:
    m: 2026-04
    v: 1
  popularity:
    sitelinks: 6
    max: 423
    pct: 1.4
  tier: long_tail
claims:
  P18:
    value: Blue Cinquefoil Knot.png
    source count: 0
    confidence: 0.0
  P31:
    value: Q1014491
    source count: 0
    confidence: 0.0
    value label: prime knot
  P31:
    value: Q1892897
    source count: 0
    confidence: 0.0
    value label: torus knot
  P31:
    value: Q4736417
    source count: 0
    confidence: 0.0
    value label: alternating knot
  P373:
    value: Cinquefoil knots
    source count: 0
    confidence: 0.0
  P646:
    value: /m/0408kdl
    source count: 0
    confidence: 0.0
  P1889:
    value: Q182186
    source count: 0
    confidence: 0.0
    value label: pentagram
  P2812:
    value: SolomonsSealKnot
    source count: 0
    confidence: 0.0
  P5350:
    value: t^2 - t + 1 - t^{-1} + t^{-2}
    source count: 0
    confidence: 0.0
  P5351:
    value: z^4 + 3z^2 + 1
    source count: 0
    confidence: 0.0
  P5352:
    value: q^{-2} + q^{-4} - q^{-5} + q^{-6} - q^{-7}
    source count: 0
    confidence: 0.0
  P6104:
    value: Q8487137
    source count: 0
    confidence: 0.0
    value label: WikiProject Mathematics
  P6366:
    value: 2777055596
    source count: 0
    confidence: 0.0
  P6432:
    value: 5_1
    source count: 0
    confidence: 0.0
  P8378:
    value: 6, 8, 10, 2, 4
    source count: 0
    confidence: 0.0
  P8416:
    value: 5a_{2}
    source count: 0
    confidence: 0.0
  P8426:
    value: 5_1
    source count: 0
    confidence: 0.0
  P8427:
    value: 5_1
    source count: 0
    confidence: 0.0
  P11034:
    value: \{-1, 2, -3, 4, -5, 1, -2, 3, -4, 5\}
    source count: 0
    confidence: 0.0
  P11035:
    value:
      amount: +5
    source count: 0
    confidence: 0.0
meta:
  wikidata id: Q5121087
  domain: prime_knot
  level: standard
  html url: https://4ort.xyz/entity/cinquefoil-knot
  markdown url: https://4ort.xyz/entity/cinquefoil-knot.md
  facts url summary: https://4ort.xyz/entity/cinquefoil-knot/facts.json
  facts url standard: https://4ort.xyz/entity/cinquefoil-knot/facts.json
  facts url full: https://4ort.xyz/entity/cinquefoil-knot/facts.json
  data source: Wikidata (CC0 / public domain)
  license: https://creativecommons.org/publicdomain/zero/1.0/
  api version: v1
  served at: 2026-08-23T21:14:57.008151Z
  entity updated at: 2026-05-03T22:54:58.348740+00:00Z
  entity created at: 2026-04-11T00:05:45.977922+00:00Z