Infinite Knots

All knot sculptures are based on closed, continuous mathematical knot structures with no beginning and no end.

Trainstation

Topological classification

Knot: K₃₀_d6881d62

Minimal crossing number: 30

Determined by exhaustive projection sweep

Dowker–Thistlethwaite code (signed)

[-22, -20, -56, 44, 54, 18, 12, -28, 38, -2, -4, 10, -30, -36, -16, -52, -50, -26, 14, 24, 48, 42, -58, 8, -32, -34, 40, -60, -6, -46]

Isometry signature

OvLLvvvwvzQvvQvQQQvQQQzPAQQkdfjkprpsCBvxsAEGEzCHGIxBDJDHFFJKMLNLNMNMLoacfdudpamgcbvuuaksaaasrfeoqddlpastjafafs

Components: 1

Knot type: nontrivial knot (single component)

Homology: Z

Hyperbolic volume: 32.3347781022278

Chern–Simons invariant: 0.132804002454061

Material: Brushed stainless steel

Dimensions: 136 × 86 × 120 cm

Weight: approx. 120 kg

Unique piece. Maintenance-free.

Suitable for permanent indoor and outdoor installation.

Viewing by appointment.

Availability & details:https://www.stainlesssteel4u.de/p/trainstation-stainless-steel-knot-sculpture-unique-piece

Infinite Knots presents a series of spatial knot structures constructed from stainless steel square tubing. All works are designed as continuous, closed-loop forms that explore geometric complexity, structural clarity, and spatial presence.

The objects are developed and fabricated using 60 mm stainless steel square tubes. Each knot is engineered as a stable, load-bearing structure and is produced through precise planning, welding, and manual finishing.

All works are fully scalable. Dimensions and proportions are adapted to the specific architectural or spatial context in which the object is installed. Custom sizes and configurations are possible upon request.

The series is continuously extended. New works are added at the top of the collection and document the ongoing development of this structural and formal investigation.

Double 6

Topological classification

Knot: K₁₂₄_e1c6dd67365f1d13

Minimal crossing number: 124

Determined by exhaustive projection sweep

Best projection axis

(0.177735, -0.983934, 0.016853)

Dowker–Thistlethwaite code (signed)

[200, 238, -232, 182, 96, -218, -104, -130, 222, 176, -226, -46, -38, -34, -32, 42, 26, 28, 80, -44, …]

DT signature (SHA256-16)

e1c6dd67365f1d13

Gauss signature (SHA256-16)

ca86b720ef77a481

Components: 1

Knot type: nontrivial knot

x = 323 cm, y = 2,34 cm, z = 323 cm

Videolink 360° turntable:

https://youtube.com/shorts/3GG1n3sJMVQ

Knot from 12 faces middlepoints of the cuboctahedron

x = 177 cm, y = 110 cm, z =196

Videolink 360° turntable:

https://youtube.com/shorts/IWFMQm7b2ok

12 corner knot

Hyperboloid based, fully symmetrical, mathematical knot.

3x3x2m³ with 60 mm squareshape.

500 kg.

Videolink 360° turntable:

https://youtube.com/shorts/MZxAUvWVWyU

Workingtitle: Octahedron to knot quadratic

It seems like completly abstract art, but it´s a symmetric, mathematical knot, as you can see.

x = 180 cm, y = 198 cm, z = 150 cm

Videolink 360° turntable:

https://youtube.com/shorts/vQMih9Qp1xU

Double Penrose Triangle

Topological classification (link)

„Two-component link with linking number 3 (orientation dependent: ±3).“

Videolink 360° turntable:

https://youtube.com/shorts/K5vuCQ-xbNY

You can find one of these, done with stainless steel, here:

https://www.stainlesssteel4u.de/p/real-penrose-triangle

IRRATIONAL

x = 3Irrational is a large-scale continuous geometric knot sculpture in brushed stainless steel.

Orthogonally interlocking linear segments generate a spatial structure of high density and internal coherence while remaining visually calm and self-contained.

The form has no fixed front; its geometry unfolds through movement and changing viewpoints.

Topological classification

Knot: K₍24₎ₓ (table index pending)

Minimal crossing number: 24

Non-alternating, prime (heuristic)

The topology is identified a posteriori from the constructed spatial curve.

Topological fingerprint

DT (SHA256-16): ce47793682c3d387

Gauss (SHA256-16): 2724cef7b806369c

x=330 cm, y = 316 cm, z = 334 cm

Weight: ca. 180 kg

Videolink 360° turntable:

https://youtu.be/DomQXXOHWpI

SPIRAL

Spiral is a continuous geometric knot structure derived from a single closed spatial curve.

The form develops through a constant directional flow and condenses into a dense, self-contained configuration without a fixed front.

The topology is not prescribed by a diagram but identified a posteriori from the constructed spatial curve.

Topological classification

Minimal crossing number: 52

Knot: K₅₂ (index pending)

Dowker–Thistlethwaite code (signed)

[-36, -64, -16, 84, 52, -26, -56, -100, 38, 94, 82, -6, 50, 54, -70, 92, -46, -62, 80, -22, -96, -72, -60, 76, -14, 86, 88, -12, 68, 32, -104, 78, -4, -48, -90, 42, 30, 58, -102, 2, -18, 40, 98, -10, 28, 74, -44, -20, -8, 24, 66, 34]

DT signature (SHA256-16): 08fc098094c15dd5

x = 172 cm, y = 180 cm, z = 170 cm

Weight: ca. 120 kg

Videolink 360° turntable:

https://youtu.be/Tf7I-BOTkSY

Ping Pong

x = 162 cm, y = 124 cm, z = 162 cm

Weight: ca. 140 kg

Topological classification: Knot K28ₓ (subindex pending)

Minimal crossing number: 28 (verified)

DT code (canonical): -48,30,-56,14,20,46,-44,-18,-36,42,-12,-6,34,40,2,50,54,-16,-24,-32,-52,8,-22,10,-4,-28,26,-38

DT signature (SHA256-16): e6bce8b75f3ad094

Structure: single closed component (one continuous strand; no link)

Consistency checks: closed loop, one connected edge component, vertex degree = 2 everywhere (no branches / no open ends).

Note: The topology is not visualised but generated by the construction.

Videolink 360° turntable:

https://youtube.com/shorts/D_05NaamFuc

Cosmic Love

Topological classification

Minimal crossing number: 36

Knot: K₃₆ (index pending)

Dowker–Thistlethwaite code (signed)

[33, 47, 23, -5, 41, 53, 59, 29, -31, -51, 49, 7, -67, 15, -57, 13, 63, -27, 55, -21, -3, -69, -65, 9, -39, 11, 19, -37, -17, -1, -71, 43, 25, -45, -35, -61]

DT signature (SHA256-16): 1d84ac07532e31ab

Gauss code

[-1, 2, -3, 5, -4, 6, 7, 4, 8, 9, 10, 11, 12, 13, 14, 15, -16, -17, 18, -19, -20, 21, -6, -7, 22, -23, -24, -14, -15, -25, 17, -12, -2, 26, -27, 24, -28, 29, -30, 20, -9, 3, 31, -32, -33, -34, -5, -8, -21, 30, 19, -10, -11, -18, -29, 28, 25, 16, -13, 1, -35, -36, -26, -31, 34, -22, 23, 33, 32, 27, 36, 35]

x = 236 cm, y = 214 cm, z= 208 cm

Weight: ca. 150 kg

Videolink 360° turntable:

https://www.youtube.com/shorts/ATFhyXrcpOQ

Topological classification

Knot: K₃₀_d6881d62

Minimal crossing number: 30

Determined by exhaustive projection sweep

Dowker–Thistlethwaite code (signed)

[-22, -20, -56, 44, 54, 18, 12, -28, 38, -2, -4, 10, -30, -36, -16, -52, -50, -26, 14, 24, 48, 42, -58, 8, -32, -34, 40, -60, -6, -46]

Isometry signature

OvLLvvvwvzQvvQvQQQvQQQzPAQQkdfjkprpsCBvxsAEGEzCHGIxBDJDHFFJKMLNLNMNMLoacfdudpamgcbvuuaksaaasrfeoqddlpastjafafs

Components: 1

Knot type: nontrivial knot (single component)

Homology: Z

Hyperbolic volume: 32.3347781022278

Chern–Simons invariant: 0.132804002454061

Material: Brushed stainless steel

Dimensions: 136 × 86 × 120 cm

Weight: approx. 120 kg

Unique piece. Maintenance-free.

Suitable for permanent indoor and outdoor installation.

Viewing by appointment.

Minimal crossing number: 30 (determined by exhaustive projection sweep)

Why Not

Topological classification

Minimal crossing number: 8

Knot: 8₁₉

Dowker–Thistlethwaite code (signed)

[-13, -9, 1, 15, 5, -7, 3, -11]

DT signature (SHA256-16): 6dd4b88d87398339

Gauss code

[1, -2, 3, -4, 5, -1, -6, 7, 4, -5, -8, 6, 2, -3, -7, 8]

Gauss signature (SHA256-16): 41ddb92480c30458

x = 162 cm, y = 128 cm, z = 144 cm

Weight: ca 70 kg

Videolink:

https://youtube.com/shorts/XOupMSveFRk

Nitro

Topological classification

Minimal crossing number: 30

Knot: K₃₀ (index pending)

Dowker–Thistlethwaite code (signed)

[5, -43, -49, 29, 47, 55, 33, -53, -39, 31, 11, 45, 51, -7, -57, -35, -13, -19, -59, 17, 25, 3, -23, -9, 1, -41, 15, 21, 37, -27]

DT signature (SHA256-16): 5fcd8d371c88a01f

Gauss code

[1, 2, 3, -4, -2, -5, -6, 7, -8, 9, 10, 11, -12, 13, 14, -15, 16, -17, -18, 19, 20, -10, -21, 22, 23, 24, -25, 6, -7, -26, -19, -27, -13, 12, 27, 18, 28, -29, 17, -16, -30, -23, 4, -3, -22, 21, -9, 8, 5, -1, -24, 30, 15, -14, -11, -20, 26, -28, 29, 25]

Gauss signature (SHA256-16): 8d1dba58089e9bb8

x = 210 cm, y = 210 cm, z = 230cm

Weight: ca. 200 kg

Videolink 360° turntable:

https://youtube.com/shorts/oCTfSffDK_k

Mirror

Mirror is just an experiment to hold all symmetries of one of famous Tamas Farkas` impossible drawings, but it´s impossible to do it.

Topological classification

Minimal crossing number: 24

Knot: K₍24₎ (index pending)

DT (signed): [-6, -14, -12, -44, -2, 4, -10, -18, 22, 32, 24, -16, 30, 38, 36, -20, 26, -28, 34, 42, -46, 8, -48, 40]

DT signature (SHA256-16): 551e517c4f28e444

Gauss signature (SHA256-16): 9d21578ace55deda

x = 210 cm, y = 170 cm, z = 272 cm

Weight: ca. 160 kg

Videolink 360° turntable:

https://youtube.com/shorts/KdTEqTRPzJg

Sundowner

152 × 90 × 172 cm

Stainless steel, approx. 200 kg

Spatial knot generated from a rule-based construction system.

The topology is constructed, not visualised.

K₍₂₈₎ (prime, non-alternating), minimal crossing number 28.

Dowker–Thistlethwaite: (-48, 30, -56, 14, 20, 46, -44, -18, -36, 42, -12, -6, 34, 40, 2, 50, 54, -16, -24, -32, -52, 8, -22, 10, -4, -28, 26, -38)

Video:

https://youtube.com/shorts/RsFKuysiNKU

Sundown

Topological classification

Minimal crossing number: 35

Knot: K₍35₎ (index pending)

DT (signed): [-18, 59, 61, -4, 68, -32, 30, -70, 2, 16, 10, 44, -42, -12, -14, -28, -22, -55, 53, 24, 26, 40, 34, 66, -64, 54, -67, -65, -20]

DT signature (SHA256-16): 2c3a92bede0e7fc2

Gauss signature (SHA256-16): 19ab2f62b8556882

x = 166 cm, y = 118 cm, y = 144 cm

Weight: ca. 100 kg

Videolink 360° turntable:

https://www.youtube.com/shorts/WCGDkGh3IhQ

XYZ

free view

Knot 8₁₉

Dowker–Thistlethwaite code: [2, 10, 6, 8, 12, 14, 4, 16]

Minimal crossing number: 8

x = 94 cm, y = 60 cm, z = 84 cm

Weight: ca. 40 kg

Videolink:

https://youtube.com/shorts/mivocmgBPaA

Front- and backside view

XYZ

Knot 8₁₉

Dowker–Thistlethwaite code: [2, 10, 6, 8, 12, 14, 4, 16]

Minimal crossing number: 8

x = 48 cm, y = 34 cm, z = 46 cm

Weight: ca. 20 kg

Videolink:

https://youtube.com/shorts/HMYgVztWlXU

Proxima B

Topological classification

Minimal crossing number: 28

Knot: K₍28₎ (index pending)

DT (signed): [36, -16, 26, 42, -10, -44, -56, -34, -20, 40, -2, -14, -32, -52, 8, -50, -54, 22, 38, -18, -28, -30, -48, -46, 12, -6, -4, -24]

DT signature (SHA256-16): 972716958220d0e9

Gauss signature (SHA256-16): f036c7fa9f00c484

x = 160 cm, y = 146 cm, z = 148 cm

Weight: ca. 150 kg

Videolink 360° turntable:

https://youtube.com/shorts/a06e8cCVmds

Always a Pleasure

Topological classification

Minimal crossing number: 26

Knot: K₍26₎ (index pending)

DT (signed): [-44, 34, 22, 40, 28, 52, 4, 24, -38, 10, 42, -32, 46, -18, 8, -48, 14, 2, 26, -30, -50, -12, -36, 16, -6, 20]

DT signature (SHA256-16): f0d65cad5797c53d

Gauss signature (SHA256-16): 05ecad5298a27faf

x= 182 cm, y = 198 cm, z = 220 cm

Weight: ca. 150 kg

Videolink 360° turntable:

https://youtube.com/shorts/nn0Ey4jK8JQ

Knots of Love

Topological classification

Minimal crossing number: 17

Knot: K₍17₎ (index pending)

DT (signed): [4, 34, -8, -10, 6, 13, -12, -18, -20, 16, 24, 26, -22, -30, -32, 28, -2]

DT signature (SHA256-16): 558be62ea85e72a3

Gauss signature (SHA256-16): 0ceaa74d7e5d3022

x = 186 cm, y = 66 cm, z = 186 cm

Weight: ca 200 kg

Videolink 360° turntable:

https://youtube.com/shorts/vSts8YeQ3AY

Celtic knot for playing

Topological classification

Minimal crossing number: 22

Knot: K₍22₎ (index pending)

DT (signed): [-18, 12, -24, -38, -36, 26, 42, -30, 44, 10, 6, 40, -34, -2, -16, -14, 4, 20, -8, 22, -32, -28]

DT signature (SHA256-16): d069ba7a135e849c

Gauss signature (SHA256-16): 4a7df45ea3077c44

x = 128 cm, y = 170 cm, z = 136 cm

Weight: ca. 80 kg

Videolink 360° turntable:

https://www.youtube.com/watch?v=0_U8wmi0tdE

Double 3

144 × 114 × 170 cm

Stainless steel, approx. 120 kg

Constructed from two mirrored modules, repeated to form six interlocking segments with 36 corners and about 20 metres (60 ft) of material.

The sculpture can be re-mounted; solid central shaft with metric M12 thread.

Topological state: K₅₀ₓ, minimal crossing number 50.

Dowker–Thistlethwaite: (88, -46, 28, -76, 100, 34, 78, -44, 48, 20, 84, -52, 62, -16, -4, -86, -10, 70, 56, 22, -24, -66, 6, 30, 64, -40, -94, -82, -36, 80, 42, -50, -26, -92, 98, 72, -32, 2, -90, -68, 96, 38, -18, 74, -8, 14, 60, 54, -58, -12).