header

Units (157)

3D | Acute Mandala | B^ | B3g | Byz | Celtic/Aura | Celtic Rosette
Celtic Wings | Compass Rose | December | Dodecahedron | Helm
Hourglass | J5-1 | Labyrinth | Mercury | Missing | Mobius | OJ
OS/IOS | OHC/OSC | Quadratic | Tao/Not Tao | Tetra Orb
Triangle | Triumvirate | Uclid | Upanishad | Vipera Star


Oriental Scale

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Oriental Scale (OS)
(M.A.I.L.)
Japanese, Captive, Orbital 3 (2.7, 5.9) (2.7, 5.9) - (3.0, 6.6+) 3.0, 6.4
(five units)
10
JDS, JDS Web base unit. Repeats into OS Dodecahedron. OrbitTR(O1) base unit.
(Tutorial)
Japanese Dragonscale Japanese Dragonscale Web (Oriental Scale Net) Oriental Scale Dodecahedron
Oriental Scale 4 (OS4) Japanese, Captive, Orbital 3   -(2.8, 7.9, 5.1)+ 2.8, 8.4, 5.6
(three units)
13
Japanese Dragonscale 4 (Shippo Tsunagi) 4-sided OS. JDS4 base unit. See also QOrbitTR(O1). Ring size-specific.
Oriental Scale 5 (OS5) Japanese, Captive, Orbital 3   -(2.8, 9.9, 4.3)+ 2.8, 9.9, 4.3 16 5-sided OS. Very ring size-specific.
Inverted Oriental Scale (IOS)
(M.A.I.L.)
Japanese, Captive, Orbital 3 (3.0, 6.4) (3.0, 6.4+) 3.0, 6.4 11
Japanese Dragonscale Contraction of/expands into JDS. Very ring size-specific. Small rings can flip out of position.
(Tutorial)
Acute Mandala
(M.A.I.L.)
Japanese, Captive, Orbital 3   (3.0, 6.1),
etc.
3.0, 6.1 (3*5)=
15
Related to JDS. Repeats into Acute Mandala Dodecahedron. Ring size specific.
(Tutorial)
Acute Mandala Dodecahedron

Captive / Orbital Cage

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Orbital Hex Cage Unit (OHCU) Japanese, Orbital 3 single: 6.0(4.8, 3.7, 5.3)+ 4.8, 3.7, 5.3
6.0
12
Orbital Hex Cage Contraction of/expands into OHC. Medium corner, small inner, large orbital rings.
Orbital Square Cage Unit (OSCU) Japanese, Orbital 3 single: 6.5 single: 6.5+ 6.5 16
Orbital Square Cage Contraction of/expands into OSC, OSCWeb. Orbital Square Cage Web
Captive Orbital Hex Cage Unit (COHCU) Japanese, Captive, Orbital 4   (6.4, 4.3, 6.4)+ 6.4, 4.3, 6.4 13
Captive Orbital Hex Cage Contraction of/expands into COHC. Large corner, small cage + captive, large orbital rings.
Captive Orbital Square Cage Unit (COSCU) Japanese, Captive, Orbital 4 2 ring: (7.0, ~9.8)(7.0, -9.9)+ 7.0, 9.9 17
Captive Orbital Square Cage Web Contraction of/expands into COSC, COSCWeb. Large captive ring.
Reverse Tao Flower
(M.A.I.L.)
Japanese, Orbital 5 6.0 6.0 - 6.1 6.0 18
Orbital 2 in 1 Chain (O1) O2-1C 6-cell loop with 3 additional center, vertical rings held in by 3 additional edge rings. Extension of OHCU, where its corner rings are singled. Not related to Tao.

Orbital Japanese

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Orbital Japanese 6 in 2 Unit (OJ6-2U) Japanese, Orbital 3  (4.8, 3.2, 4.8),
etc.
4.8, 3.2, 4.8 11
Orbital Japanese 6 in 2 3 orbital connections on doubled center ring set. Contraction of/expands into OJ6-2. Ring size specific.
Orbital Japanese 8 in 2 Unit (OJ8-2U) Japanese, Orbital 3  (7.0, 4.1, 5.4),
etc.
7.0, 4.1, 5.4 14
Orbital Japanese 8 in 2 4 orbital connections on doubled center ring set. Contraction of/expands into OJ8-2. Ring size specific.
Orbital Japanese 10 in 2 Unit (OJ10-2U) Japanese, Orbital 3  (9.5, 4.3, 5.6),
etc.
9.5, 4.3, 5.6 17 5 orbital connections on doubled center ring set. Ring size specific.
Orbital Japanese 12 in 2 Unit (OJ12-2U) Japanese, Orbital 3  (12.5, 4.5, 5.8),
etc.
12.5, 4.5, 5.8 20
Orbital Japanese 12 in 2 6 orbital connections on doubled center ring set. Contraction of/expands into OJ12-2. Ring size specific.

Orbital Unit / Celtic Rosette

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Orbital Unit 3
(Trillium)**
Japanese, Orbital 2   5.5 5.5 6
Directional swirl of 3 basic orbital connections with each orbiting off the last orbital ring. Adding one reinforced ring on each side yields Tao 3 **M.A.I.L. entry "Trillium" contains three additional rings.
(Tutorial (step 1-6))
Tao 3
Orbital Unit 4
(Orbital Square Sheet)**
Japanese, Orbital 2   5.5 5.5 8 Directional swirl of 4 basic orbital connections with each orbiting off the last orbital ring. **M.A.I.L. entry for "Orbital Square Sheet" is a repeated square grid.
Orbital Unit 5 Japanese, Orbital 2 single: 5.6 5.7 5.7 10 Directional swirl of 5 basic orbital connections with each orbiting off the last orbital ring. AR specific.
Orbital Unit 6 Japanese, Orbital 2 single: 6.0 6.0 6.0 12 Directional swirl of 6 basic orbital connections with each orbiting off the last orbital ring. Very AR specific.
Orbital Unit 7 Japanese, Orbital 2   6.3 6.3 14 Directional swirl of 7 basic orbital connections with each orbiting off the last orbital ring. Very AR specific.
Celtic Rosette 4
(M.A.I.L.)
Japanese, Orbital 2   5.5 5.5 8 Directional swirl of 4 basic orbital connections with each orbiting off the last orbital ring. Each edge ring also links the successive orbital ring. Slight doming in sample displayed.
Celtic Rosette 5
(M.A.I.L.)
Japanese, Orbital 2   5.5 5.5 10 Directional swirl of 5 basic orbital connections with each orbiting off the last orbital ring. Each edge ring also links the successive orbital ring.
Celtic Rosette 6
(M.A.I.L.)
Japanese, Orbital 2 single: 5.5 5.5 5.5 12 Directional swirl of 6 basic orbital connections with each orbiting off the last orbital ring. Each edge ring also links the successive orbital ring.
Celtic Rosette 7
(M.A.I.L. gallery)
Japanese, Orbital 2 single: 5.7 5.7 5.7 14 Directional swirl of 7 basic orbital connections with each orbiting off the last orbital ring. Each edge ring also links the successive orbital ring.

Helm+

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Helm Unit 3 Japanese, Orbital 3  (3.2, 5.5, 6.5) 3.2, 5.5, 6.5 11
Helm Chain 3-way Helm Chain junction. Contraction of/expands into Helm Chain Web. Helm Chain Web
Helm Unit 4 Japanese, Captive, Orbital 3  (3.2, 5.5, 8.7) 3.2, 5.5, 8.7 14
Helm Chain 4-way Helm Chain junction. Contraction of/expands into Helm Square Sheet.
Helm Unit 5 Japanese, Captive, Orbital 3  (3.2, 5.5, 11.1) 3.2, 5.5, 11.1 17
Helm Chain 5-way Helm Chain junction. Contraction of/expands into Helm-5 Dodecahedron. Helm-5 Dodecahedron
Helm Unit 6 Japanese, Captive, Orbital 3  (3.2, 5.5, 13.4) 3.2, 5.5, 13.4 20
Helm Chain 6-way Helm Chain junction. Contraction of/expands into Helm Hex Sheet. Helm Hex Sheet
Helm Loop 3 Japanese, Captive, Orbital 3  (3.3, 5.5, 13.4) 3.3, 5.5, 13.4 15
3-cell Helm Chain loop. Contraction of/expands into Helm Hex Sheet, Helm-5 Dodecahedron.
Helm Chain Helm Hex Sheet Helm-5 Dodecahedron
Helm Loop 4 Japanese, Captive, Orbital 3  (3.2, 5.5, 7.7) 3.2, 5.5, 7.7 20
Helm Chain 4-cell Helm Chain loop. Contraction of/expands into Helm Square Sheet.
Helm Loop 5 Japanese, Captive, Orbital 3  (3.2, 5.5, 6.5) 3.2, 5.5, 6.5 25
Helm Chain 5-cell Helm Chain loop. Contraction of/expands into Helm Dodecahedron. Helm Dodecahedron
Helmi Loop 3 Japanese, Captive, Orbital 4  (5.3, 7.4, 9.0, 11.1) 5.3, 7.4, 9.0, 11.1 21
3-cell Helmi loop.
Helmi Loop 4 Japanese, Captive, Orbital 4  (5.3, 7.4, 8.1) 5.3, 7.4, 8.1 28
4-cell Helmi loop.
Helmi Loop 5 Japanese, Captive, Orbital 4  (5.3, 7.4, 6.9) 5.3, 7.4, 6.9 35
5-cell Helmi loop.

Hourglass+

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Hourglass Unit (HGU)
(M.A.I.L.)
(Maillepedia)**
Japanese, Orbital 3 single: ~6.6 6.6+ 7.0
(four units)
8
Orbital 2 in 1 Chain (O1) O2-1C loop. Folds inside out starting at 6.9 AR. Pentagonally tessellates as Hourglass Dodecahedron. **Maillepedia entry has four additional rings: one on each corner.
(Tutorial), (2)
Hourglass Dodecahedron
Hourglass Unit (2) Japanese, Orbital 3 single: 6.7 6.7+ 6.7 10
HGU with 2 rings in each of 2 horizontal sets. Contraction of/expands into OHCWeb, OSC, Hourglass Hex (2). Pentagonally tessellates as Hourglass Dodecahedron (2).
(Tutorial), (2)
Orbital Square Cage Orbital Hex Cage Web (Hourglass Web) Hourglass Dodecahedron (2)
Hourglass Unit (3) Japanese, Orbital 4 single: 7.0 7.0+ 7.0 12
HGU with 3 rings in each of 2 horizontal sets (oriented vertically in sample image). Pentagonally tessellates as Hourglass Dodecahedron (3).
(Tutorial), (2)
Hourglass Dodecahedron (3)
Hourglass Unit (4) Japanese, Orbital 4   7.5 7.5, 7.1 14 HGU with 4 rings in each of 2 horizontal sets (oriented vertically in sample image).
(Tutorial), (2)
Hourglass Hex Japanese, Orbital 5  ~6.8 6.8, 6.6 36 HGU repeated into a 6-sided unit. AR-sensitive.
Hourglass Hex (2) Japanese, Orbital 5 single: 7.1 7.2 - 7.5 7.3 42
Orbital Hex Cage Web (Hourglass Web) Contraction of/expands into OHCWeb. HGU(2) repeated into a 6-sided unit. AR-sensitive.
Image (Missing) Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Missing Half An Hour Unit Japanese, Orbital 5 single: 6.86.8+ 6.8 16 Contraction of/expands into Missing Half An Hour.
Missing Half An Hour Unit (2) Japanese, Orbital 5 single: 7.07.0+ 7.0 20
Missing Half An Hour (2) Doubled horizontal rings. Contraction of/expands into Missing Half An Hour (2).
Missing Half An Hour Square Unit (2) Japanese, Orbital 5 2-ring: (10.3, 7.6)(10.3, 7.6)+ 10.3, 7.6 26
Missing Half An Hour Square Sheet (2) Doubled horizontal rings. Contraction of/expands into Missing Half An Hour Square Sheet (2).

Tao / Not Tao

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Tao 3
(M.A.I.L.)**
(Maillepedia)
Japanese, Orbital, Reinforced 3   -(4.3, 5.5)+ 4.3, 5.5 8
Orbital Unit 3 Is Orbital Unit 3 with 2 added reinforced rings, one on each side. Contraction of/expands into Tao 3 Sheet. **M.A.I.L. entry is multiple units bolted together in a chain sequence.
(Tutorial), (Video)
Tao 3 Sheet
Inverted Tao 3 Japanese, Orbital, Reinforced 3    7.0, 5.8 10 Tao 3 unit with single reinforced ring on the inside and doubled corner rings.
Not Tao 2 (NT2) Japanese, Reinforced 3     4.5 6
4-cell 2-1C loop with reinforced rings on each side. Repeated chain sequence as Bee Stings, Scary Weave, Honey Bee.
(Tutorial)
Bee Stings Scary Weave Honey Bee
Not Tao 3 (NT3)
(M.A.I.L.)
(Maillepedia)
Japanese, Reinforced 3  -(4.2, 5.5)+
-(3.2, 5.6, 6.7)+
3.2, 5.6, 6.7
4.2, 5.5
8
6-cell 2-1C loop with reinforced rings on each side. Contraction of/expands into NT3S. Repeats into NT3Web, NT3 Dodecahedron. Related to Upanishad Unit.
(Tutorial), (2)
Not Tao 3 Sheet Not Tao 3 Web Not Tao 3 Dodecahedron Upanishad Unit
Not Tao 4 (NT4)
(M.A.I.L.)
Japanese, Reinforced 3  -(3.4, 9.0, 7.0)+ 3.4, 9.0, 7.0
2WD
10 8-cell 2-1C loop with reinforced rings on each side. 4-sided NT3.
Not Tao 5 (NT5)
(M.A.I.L.)
Japanese, Reinforced 3    2WD** 12 10-cell 2-1C loop with reinforced rings on each side. 5-sided NT3. **2WD: .048" 13/64", .062" 1/2", 9/32" (mandrels listed).
(Tutorial)
Not Tao 6 (NT6)
(M.A.I.L.)
Japanese, Reinforced 3    2WD** 14 12-cell 2-1C loop with reinforced rings on each side. 6-sided NT3. **2WD: .062" .602", .048" 13/64", .062" 9/32" (mandrels listed).
(Tutorial)
Not Tao 7 (NT7) Japanese, Reinforced 3    2WD** 16 14-cell 2-1C loop with reinforced rings on each side. 7-sided NT3. **2WD: .062" .708", .048" 13/64", .062" 9/32" (mandrels listed).
Not Tao 8 (NT8) Japanese, Reinforced 3    2WD** 18 16-cell 2-1C loop with reinforced rings on each side. 8-sided NT3. **2WD: .062" .708", .048" 13/64", .062" 29/128" (mandrels listed).
Not Tao 9 (NT9) Japanese, Reinforced 3    3WD** 20 18-cell 2-1C loop with reinforced rings on each side. 9-sided NT3. **3WD: .080" .850", .048" 15/64", .062" 7/32" (mandrels listed).
Upanishad Unit
(M.A.I.L.)
Japanese, Reinforced 5  (3.2, 3.0, 6.7, 5.6), etc. 3.2, 3.0, 6.7, 5.6 (3*6)=
18
Not Tao 3 Sheet Contraction of/expands into NT3S. Related to NT3. Ring size specific. Not Tao 3 (NT3)

Borealis / Celtic Visions+

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Aura Unit
(M.A.I.L.)**
(Maillepedia)
Japanese 3    3.0, 5.6 13
Contraction of/expands into Borealis, CWeb, Aura Dodecahedron. Unstable as a standalone. **M.A.I.L. entry is multiple units bolted together in chain sequence.
Borealis Celtic Web Aura Dodecahedron
Inverted Aura
(M.A.I.L.)
(Maillepedia)
Japanese 3 (3.0, >5.6)(3.0, -6.0+) 3.0, 6.0 11
Borealis Contraction of/expands into Borealis, Inverted Aura Dodecahedron.
Celtic Circle 3 (Borealis Unit)
(M.A.I.L.)
Japanese 4  (-3.3, -8.3+),
(2WD)
3.3, 8.3 (3*7)=
21
3-cell Celtic chain loop. Contraction of/expands into Borealis. See also Triangle.
Celtic Borealis Triangle
Celtic Circle 4 (CC4) Japanese 4 (3.0, >5.1)-(3.1, 5.5)+ 3.1, 5.5 (4*7)=
28
Celtic 4-cell Celtic chain loop.
Celtic Circle 5 (CC5) Japanese 4  -(3.1, 5.1)+ 3.1, 5.1 (5*7)=
35
Celtic 5-cell Celtic chain loop.
Celtic Visions Circle 4 (CVC4)
(M.A.I.L.)
Japanese 5 3.0, 6.1(3.0, 6.1) - (3.3, 6.6) 3.3, 6.3 (4*8)=
32
Celtic Visions 4-cell CV chain loop.
Celtic Visions Circle 5 (CVC5)
(M.A.I.L.)
Japanese 5  (3.0, 5.5) - (3.3, 6.0) 3.0, 5.5 (5*8)=
40
Celtic Visions 5-cell CV chain loop. Adding corner rings produces CVC5Star. Celtic Visions Circle 5 Star
Inverted Aura 4
(M.A.I.L.)
Japanese 3    2WD 14 4-sided Inverted Aura. Very ring size specific, or use smaller ring sizes + additional small stabilizer rings around the edge.
Image (Uclid) Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Uclid Loop 3 Japanese 4  (3.3, 5.5, 13.4) 3.5, 5.5 15
Uclid 3-cell Uclid loop.
Uclid Loop 4 Japanese 4  (3.2, 5.5, 7.7) 3.2, 5.5, 7.7 20
Uclid 4-cell Uclid loop.

Byzantine+

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Byzantine 3 Unit (Byz3U) European 4    3.3, 4.0 (3*6+2)=
20
Byzantine 3 Byz cells off central doubled ring set. Contraction of/expands into Byz Web. Byzantine Web
Byzantine 4 Unit (Byz4U) European 4    3.3, 5.4 (4*6+2)=
26
Byzantine 4 Byz cells off central doubled ring set. Contraction of/expands into Byz Web Square. Byzantine Web Square
Byzantine 5 Unit (Byz5U) European 4    3.3, 7.0 (5*6+2)=
32
Byzantine 5 Byz cells off central doubled ring set. Pentagonally tessellates as Byz Dodecahedron. Byzantine Dodecahedron
Byzantine 6 Unit (Byz6U) European 4    3.2, 8.5 (6*6+2)=
38
Byzantine 6 Byz cells off central doubled ring set. Contraction of/expands into Byz Web Triangle. Byzantine Web Triangle

December/Celtic Labyrinth

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
December 3 European 5  (3.6, 4.5, 7.4) 3.6, 4.5, 7.4 23 Byz3U with added corner rings spreading open Byz terminated ends.
December 4 (Celtic Labyrinth), (Byzantine Diamond)
(M.A.I.L.)
(Maillepedia)**
European 5  (3.6, 6.6) 3.6, 6.6 30 Byz4U with added corner rings spreading open Byz terminated ends. **Maillepedia entry is bolted sequence of units.
(Tutorial), (Video)
December 5
(M.A.I.L. gallery)
European 5  (3.6, 8.7) 3.6, 8.7 37 Byz5U with added corner rings spreading open Byz terminated ends.
(Video)
December
(M.A.I.L.)
European 5  (3.6, 11.1) 3.6, 11.1 44 Byz6U with added corner rings spreading open Byz terminated ends.
December 7 European 5  (3.5, 12.1) 3.5, 12.1 51 Byz7U with added corner rings spreading open Byz terminated ends.
December 8 European 5  (3.5, 13.4) 3.5, 13.4 58 Byz8U with added corner rings spreading open Byz terminated ends.
December 9 European 5    2WD 65 Byz9U with added corner rings spreading open Byz terminated ends.
December 10 European 5    2WD 72 Byz10U with added corner rings spreading open Byz terminated ends.

B^

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
B^3
(M.A.I.L.)**
Japanese, European 4 >4.4-4.7 4.7 (3*8)=
24
B^ Chain 3-cell B^ Chain loop. Repeats into B^3 Web. **M.A.I.L. entry has inside set of rings singled. Bł Web
B^2 (B^4)
(M.A.I.L.)
Japanese, European 5  4.1 4.1 (4*8)=
32
B^ Chain 4-cell B^ Chain loop. Ring size specific.
(Video)
B^5 Japanese, European 5  (4.0, 3.6) 4.0, 3.6 (5*8)=
40
B^ Chain 5-cell B^ Chain loop. Very ring size specific.
B^3+1 Japanese, European 6  (4.2, 3.9, 4.1) 4.2, 3.9, 4.1 22** B^3 unit with an added central (hidden in picture) ring. **singled connectors.
B^2+1 (B^4+1)
(M.A.I.L.)
Japanese, European 4 4.44.4 4.4 33 B^2 unit with an extra ring in the middle for structure. Ideal chess king topper.
(Tutorial)
B^5+1 Japanese, European 6  (6.9, 4.4, 3.7) 6.9, 4.4, 3.7 41 B^5 with added central ring.
B^6+1 Japanese, European 6  (8.7, 4.5, 3.7) 8.7, 4.5, 3.7 49 B5+1 side adding progression.
B^7+1 Japanese, European 6  (11.1, 4.5, 3.7) 11.1, 4.5, 3.7 57 B6+1 side adding progression.
B^8+1 Japanese, European 6  (13.4, 4.5, 3.7) 13.4, 4.5, 3.7 65 B7+1 side adding progression.
B^9+1 Japanese, European 6    2WD 73 B8+1 side adding progression.
B^10+1 Japanese, European 6    2WD 81 B9+1 side adding progression.

B^ G-Units

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
B3g European 4  (5.5, 4.0, 4.9) 5.5, 4.0, 4.9 (3*5)+2=
17
Inverted B^3 unit.
B2g (B4g)
(M.A.I.L.)
European 4  (6.5, 4.1, 4.2) 6.5, 4.1, 4.2 (4*5)+2=
22
B3g side adding progression.
B5g European 4  (8.4, 4.1, 4.2) 8.4, 4.1, 4.2 (5*5)+2=
27
B4g side adding progression.
B6g European 4  (11.1, 4.1, 4.4) 11.1, 4.1, 4.4 (6*5)+2=
32
B5g side adding progression.
B7g European 4  (13.4, 4.1, 4.2) 13.4, 4.1, 4.2 (7*5)+2=
37
B6g side adding progression.
B8g European 4    2WD (8*5)+2=
42
B7g side adding progression.
B9g European 4     2WD (9*5)+2=
47
B8g side adding progression.

B^ / G-Unit Combo

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
B2g^2 Japanese, European 7  (5.8, 4.7, 3.7, 4.2) 5.8, 4.7, 3.7, 4.2 27 Alternates between B^ and B#g knots. Large center ring.
B3g^3 Japanese, European 7  (9.0, 4.5, 3.7, 4.2) 9.0, 4.5, 3.7, 4.2 43 Alternates between B^ and B#g knots. Large center ring. Very ring size specific.
B4g^4 Japanese, European 7  (13.4, 4.5, 3.9, 4.2), 2WD 13.4, 4.5, 3.9, 4.2 57 Alternates between B^ and B#g knots. Large center ring. Very ring size specific.

Vipera Star

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count See also: Berus (weaves).
Vipera Star 3 European, Spiral 3 (3.6, 4.5) (3.6, 4.5)+ 3.6, 4.5 13
Berused 2-1Chain wrapped around a central ring. Is basis of Hoodoo Hex (without center ring). Hoodoo Hex
Vipera Star
(M.A.I.L.)
European, Spiral 3 ~(3.6, 5.6) (3.6, 5.6) - (3.8, 6.0) 3.6, 5.6 17
Berused 2-1Chain wrapped around a central ring. Is basis of Hoodoo Sheet (without center ring).
(Tutorial), (Video)
Hoodoo Sheet
Vipera Star 5 European, Spiral 3   (3.6, -7.1) 3.6, 7.1 21 Berused 2-1Chain wrapped around a central ring.
Vipera Star 6 European, Spiral 3   (3.6, <9.3) 3.6, 9.3 25 Berused 2-1Chain wrapped around a central ring.
Vipera Star 7 European, Spiral 3   (3.6, -11.1) 3.6, 11.1 29 Berused 2-1Chain wrapped around a central ring.
Vipera Star 8 European, Spiral 3   (3.6, -13.4) 3.6, 13.4 33 Berused 2-1Chain wrapped around a central ring.
Vipera Star 9 European, Spiral 3     3.6, 15.6** 37 Berused 2-1Chain wrapped around a central ring. **Large ring slightly oversized in sample.

Extended

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Note
Quadratic 2 in 1 Unit
(M.A.I.L.)
(Maillepedia)
Spiral 1  -8.4 - 8.7 set 4 4-ring 2-1C forced spiral unit.
Minerva Unit
(Minverva), (Byz Double Knot)**
European 6   5.0 - 5.1 5.0 10
8-cell 4-2C folded back completely and locked in place with two additional rings. **Single unit as found in Minerva, and Byz Double Knot chains.
(Tutorial), (Video)
MinervaByzantine Double Knot
Mercury Unit
(M.A.I.L.), (2-1 ByzCaptive)
(Maillepedia), (2-1 ByzCaptive)**
Japanese, European 2 single: ~3.8 3.9 3.9 6
2-ring 2-1C segment with 4-ring "Box" enclosure. Integrates into Hoodoo Chain. Repeats as Mercury. **M.A.I.L., and Maillepedia entries are chain sequences. Mercury (Chain)
Compass Rose
(M.A.I.L.)
(Maillepedia)
European, Spiral, Captive 5     2WD** 58
Hoodoo Chain Hoodoo Chain loop surrounds 2 central captive rings. 8 protruding rings. Very ring size specific. **2WD: .062" 3/16", .100" 7/16" - not entirely stable: captives can be forced out. Minimum security prison.
Celtic Wings Flower
(M.A.I.L. gallery)
Japanese 4   (3.5, 5.5) 3.5, 5.5 48
6-cell Celtic Wings loop. Edge ring size variable.
Celtic Star
(M.A.I.L.)
Japanese 6  -(3.3, 5.5)+ 3.3, 5.5 (5*9)=
45
Celtic Visions Circle 5 CVC5 unit with rings added to 5 outside corners. Center ring(s) optional.
(Video)
Triangle
(M.A.I.L.)
Japanese, European 6    2WD (3*9)=
27
Celtic Circle 3 (CC3) (Borealis Unit) CC3 with visions (CVC3 doesn't work well on its own), added corners, and enhanced edges.
(Tutorial)
Triumvirate
(M.A.I.L.)
Japanese, Orbital 6    2WD
2WD
29
Japanese 3 in 1 Built off J3-1. 3 ring sizes in most cases, ideally in multiple WDs. Sample: .062" aluminum 1/8", 1/4", .080" copper 1/4".
(Tutorial)
Triumvirate (2) Japanese, Orbital 6    2WD 50
Japanese 6 in 2 (J6-2) Built off J6-2. 5 ring sizes used in sample: .062" 3/16", 7/32", 1/4", and .080" 13/32", 5/16" (mandrels listed).
Helmish Aura Unit
(M.A.I.L.)**
Japanese, Orbital 9   (3.1, 5.8) 3.1, 5.8 38 2 Aura units connected with, and terminated by Helm Chain segments. **M.A.I.L. entry for Helmish Aura is a chain sequence.
Airplane
(M.A.I.L.)
European, Japanese 6   (5.3, 4.8, 4.0, 3.6), etc. 5.3, 4.8, 4.0, 3.6 14 Extended unit.
(Tutorial)

3D

Orb

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Samples Ring Count
Repeats into Tetra Orb Cube.Tetra Orb Cube (2)
Tetra Orb
(M.A.I.L.)
(Maillepedia)
Japanese, Orbital 3 single: 6.06.0 - 6.1+ 6.0 (4+6*2)=
16
4-ring tetrahedron core. 6 edges each have an orbital ring held in place by a protruding ring.
(Tutorial)
Tetra Orb (2) Japanese, Orbital 3 single: 6.26.2 - 6.6 6.2 (4+6*3)=
22
Double protruding rings. Dimensionalises as TOT Cube. Repeats into Tetra Orb Cube (2).
(Tutorial).
TOT Cube
Tetra Orb (3) Japanese, Orbital 4 single: 6.66.6+ 6.7 (4+6*4)=
28
Triple protruding rings.
(Tutorial)
Image (Johnson Solid) Family/Sub Ring
Types
Minimum AR Ideal AR1 Samples Ring Count Note
Johnson Solid Steel Ball
(M.A.I.L.)
Japanese, Orbital 3 single: 6.76.7 - 7.0 6.7
(2)
(6+9*2)=
24
6-ring hedron core. 9 edges each have an orbital ring held in place by a protruding ring.
Johnson Solid Steel Ball (2) Japanese, Orbital 3 single: 6.86.8 - 7.0+ 6.8
(2)
(6+9*3)=
33
Double protruding rings.
Johnson Solid Steel Ball (3) Japanese, Orbital 4 single 7.37.3+ 7.3
(2)
(6+9*4)=
42
Triple protruding rings.
Image (Octa) Family/Sub Ring
Types
Minimum AR Ideal AR1 Samples Ring Count Note
Octa Orb Japanese, Orbital 3 single: 7.07.0 7.0
(2)
(8+12*2)=
32
8-ring octahedron core. 12 edges each have an orbital ring held in place by a protruding ring.
Octa Orb (2) Japanese, Orbital 3  7.3 - <7.8 7.3
(2)
(8+12*3)=
44
Double protruding rings.
Octa Orb (3) Japanese, Orbital 4  7.8+ 7.8 (8+12*4)=
56
Triple protruding rings.
Image (Hexa) Family/Sub Ring
Types
Minimum AR Ideal AR1 Samples Ring Count Note
Hexa Orb Japanese, Orbital 3    9.3, 5.8, 4.3
(2) (3)
(6+12*2)=
30
6-ring hexahedron (cube) core. 12 edges each have an orbital ring held in place by a protruding ring.
Hexa Orb (2) Japanese, Orbital 3    9.3, 6.7, 5.5
(2)
(6+12*3)=
42
Double protruding rings. Sample is a bit loose.
Hexa Orb (3) Japanese, Orbital 4    11, 7.0, 5.9, 5.7
(2) (3)
(6+12*4)=
54
Triple protruding rings.
Image (Dodeca) Family/Sub Ring
Types
Minimum AR Ideal AR1 Samples Ring Count Note
Dodeca Orb (2) Japanese, Orbital 3     13, 7.0, 5.9
(2)
102 12-ring dodecahedron core. 30 edges each have an orbital ring held in place by protruding rings, doubled.

Dodecahedron

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR1 Sample Ring Count Plus Dodeca Orb, just above.
Japanese 5 in 1 (J5-1)
(M.A.I.L.)
Japanese 2     2.1, 2.7 42 Cross between J4-1, and J6-1. Forced dodecahedron.
(Tutorial), (Video)
Japanese 10 in 2 (J10-2) Japanese 3     2.7, 4.7, 5.4** 84 Kinged J5-1. Cross between J8-2, and J12-2. Forced dodecahedron. **Large ring pair has smaller ring on inside.
(Video)
Celtic Visions Dodecahedron
(M.A.I.L.)
Japanese 6     2WD
(2)
242
Celtic Visions CV-based. CVWeb with pentagonal tessellation. a.k.a. "Celtic Rose Sheet (Pentagonal Tessellation)". Celtic Visions Web
Aura Dodecahedron Japanese 4     3.2, 5.0, 5.8 180
Aura Unit Aura units forming dodecahedron. CWeb with pentagonal tessellation. CV Dodecahedron without the "visions" rings. Celtic Web
Inverted Aura Dodecahedron Japanese 4     3.1, 5.0, 6.0, 6.3 180
Inverted Aura Inverted Aura units forming dodecahedron.
Helm Dodecahedron Japanese, Captive, Orbital 4     3.5, 5.9, 6.6, 7.5 130
Helm Chain Helm Chain-based. Helm Chain Web with pentagonal tessellation. Helm Chain Web
Helm-5 Dodecahedron Japanese, Captive, Orbital 4  (2WD) 3.5, 5.9. 11.0, 12.5 114
Helm Unit 5 Helm Unit 5 expanded into a dodecahedron. Ring size specific.
Orbital Japanese 6 in 2 Dodecahedron
(M.A.I.L.)
Japanese, Orbital 4     3.2, 4.9, 5.3 160
OJ6-2U forming dodecahedron. OJ6-2 with pentagonal tessellation. Ring size specific. Orbital Japanese 6 in 2
Hourglass Dodecahedron Japanese, Orbital 3 single: 6.9 or 7.0 6.9? - 7.0 7.0 140
Hourglass Unit Hourglass Units with pentagonal tessellation forced into a sphere.
(Tutorial)
Hourglass Dodecahedron (2)
(M.A.I.L.)
Japanese, Orbital 3 single: 7.1 7.1 - 7.2 7.4, 7.3, 6.6
7.1
160
Hourglass Unit (2) Double center rings. Hourglass Unit (2) with pentagonal tessellation forced into a sphere. Related to OHC, OHCWeb.
(Tutorial)
Orbital Hex Cage Web (Hourglass Web)
Hourglass Dodecahedron (3) Japanese, Orbital 4 single: 7.7 7.7+ 7.7 180
Hourglass Unit (3) Triple center rings. Hourglass Unit (3) with pentagonal tessellation forced into a sphere.
(Tutorial)
Orbital Hex Cage Unit Dodecahedron Japanese, Orbital 4     6.0, 6.2, 6.8 160
Orbital Hex Cage Unit OHCU forming dodecahedron. OHCUWeb with pentagonal tessellation. Ring size specific. Orbital Hex Cage Unit (OHCU) Web
Orbital Pentagonal Cage Unit Dodecahedron Japanese, Orbital 3    8.7, 7.3, 6.4 110 5-sided OHC/OSC unit forming dodecahedron.
Acute Mandala Dodecahedron Japanese, Orbital 4   (3.1, 6.2, <8.7, <9.5) 3.1, 6.2, 8.7, 9.5 240
Acute Mandala Acute Mandala units forming dodecahedron. Very ring size specific.
Oriental Scale (OS) Dodecahedron
(M.A.I.L. gallery)
Japanese, Orbital 4   (3.2, 6.9, 5.8) 3.2, 6.9, 5.8 120
Oriental Scale OS units forming dodecahedron. JDS Web with pentagonal tessellation.
Not Tao 3 (NT3) Dodecahedron
(M.A.I.L.)
Japanese, Reinforced 4   (4.2, 4.7, 5.0) 4.2, 4.7, 5.0 120
Not Tao 3 (NT3) NT3 units forming dodecahedron. NT3 Web with pentagonal tessellation. Not Tao 3 Web (NT3 Web)
M3 Dodecahedron Spiral/Mobius 1 ~2.3 2.4 2.4 60
Mobius 3s repeated into a dodecahedron. M3 with pentagonal tessellation. Ring size-specific. Sample is wrapped around a marble for stability. M3
Hoodoo Dodecahedron Spiral 3   3.0 3.0 240
Hoodoo Chain Hoodoo Chain-based dodecahedron. Hoodoo Web with pentagonal tessellation. Ring size specific. Hoodoo Web
4 Winds Dodecahedron Persian 3   (3.1, 7.7) 3.1, 7.7 192
4 Winds 4 Winds segments forming doecahedron. 4 Winds Hex Sheet with pentagonal tessellation instead. 4 Winds Hex Sheet
Byzantine Dodecahedron European 4  (3.3, 7.2) 3.3, 7.2 324
10-ring Byz segments tessellated pentagonally, continued into a sphere. Byz5U forming dodecahedron. Byz Web with pentagonal tessellation.
Byzantine Byzantine 5 Unit Byzantine Web
Trizantine Dodecahedron European 7   <(4.3, 5.4, 6.1, 10.8) 4.3, 5.4, 6.1, 10.8 444
Trizantine (Triz) 14-ring Triz segments tessellated pentagonally, continued into a sphere. Triz Web with pentagonal tessellation. Ring size specific. Sample is loose. Trizantine Web

Mobius

Image Name Family/Sub Ring
Types
Minimum AR Ideal AR Sample Ring Count
Spiral 4 in 1 Basis of many Spiral weaves. Spiral 4 in 1 Web
Mobius Ball  
(M.A.I.L.)
(Maillepedia)
Spiral/Mobius 1   -6.0 - 14.0+ 14 variable Sphere composed of several same-size rings, with each passing through every other ring, consistently leaning in the same direction.
(Tutorial), (2)
Mobius 3 Spiral/Mobius 1 2.02.1+ table 3
Three ring mobius. Base construct of Hoodoo Hex, Voodoo Hex. Repeats into M3, Dragog. Chain sequenced as Mobius Chain, Flower, Daisy Chain 1, Daisy Chain 2. These "units" sometimes replaces single rings in weaves to modify their appearance/behaviour.
Hoodoo Hex Voodoo Hex M3 Dragog Mobius Chain Flower Daisy Chain 1 Daisy Chain 2
Mobius 4 Spiral/Mobius 1 2.4 or 2.52.5+ table 4
Four ring mobius. Spiral 4 in 1 basis. Base construct of Hoodoo (Sheet), Voodoo. Repeats into Brejao Flowers, Dragog Square, Dragog Square Web. Chain sequenced as Fourever Chain.
Spiral 4 in 1 Hoodoo (Sheet) Voodoo Brejao Flowers Dragog Square Dragog Square Web Fourever Chain
Mobius 5 Spiral/Mobius 1 3.03.1+ table 5 Five ring mobius. Base construct of Moorish Rose Dodecahedron.
Mobius 6 Spiral/Mobius 1 3.23.3+ table 6
Six ring mobius. Spiral 6 in 1 basis. Base construct of Moorish Rose. Repeats into M6.
Spiral 6 in 1 Moorish Rose M6
Mobius 7 Spiral/Mobius 1 3.6 or 3.73.7+ table 7 Seven ring mobius.
Mobius 8 Spiral/Mobius 1 3.94.0+ table 8
Spiral 8 in 1 Eight ring mobius. Spiral 8 in 1 basis.
Mobius 9 Spiral/Mobius 1 4.24.3+ table 9 Nine ring mobius.
Mobius 10 Spiral/Mobius 1 4.5 or 4.64.6+ table 10 Ten ring mobius.


3D | Acute Mandala | B^ | B3g | Byz | Celtic/Aura | Celtic Rosette | Celtic Star
Celtic Wings | Compass Rose | December | Dodecahedron | Helm
Hourglass | J5-1 | Labyrinth | Mercury | Missing | Mobius | OJ
OS/IOS | OHC/OSC | Quadratic | Tao/Not Tao | Tetra Orb
Triangle | Triumvirate | Uclid | Upanishad | Vipera Star



1Ideal AR:

Units tend to be AR-specific, and many use multiple ring types. Experiment with different ring sizes and wire diameters to find a good fit.