Units (79)

OS/IOS | OJ | Celtic Rosette | OHC/OSC
Hourglass | Missing | Tao/Not Tao
Borealis/Celtic/CV | Byz | B3/B2
Tetra Orb | Dodecahedron
Mobius

  Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Sample Ring Count Note
Quadratic 2 in 1 Unit Spiral 1  8.4 - 9.1 set 4 4-ring 2-1C forced spiral unit.
Mercury Unit Japanese, European 2 single: ~3.83.9 3.9 6
2-ring 2-1C segment with 4-ring "Box" enclosure. Connects in a series as Mercury, 2-1 ByzCaptive. Mercury (Chain)
OS/IOS
(5)
NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing CountNote
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
Japanese DragonscaleContraction of JDS. OrbitTR(O1) base unit. Tutorial.
Oriental Scale 4 (OS4) Japanese, Captive, Orbital 3  -(2.8, 7.9, 5.1)+ 2.8, 8.4, 5.6
(three units)
+3= 13
Japanese Dragonscale 4 (Shippo Tsugari)4-sided OS. Contraction of JDS4. QOrbitTR(O1) base unit.
Oriental Scale 5 (OS5) Japanese, Captive, Orbital 3  -(2.8, 9.9, 4.3)+ 2.8, 9.9, 4.3 +3= 16 5-sided OS.
Inverted Oriental Scale (IOS)
(M.A.I.L.)
Japanese, Captive, Orbital 3 3.0, 6.43.0, 6.4+ 3.0, 6.4 11 Contraction of JDS. Not completely stable: small rings flip to either side. 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. Ring size specific. Tutorial
Orbital
Japanese (4)
Name Family/Sub Ring
Type
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 23 orbital connections on doubled center ring set. Contraction of 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 24 orbital connections on doubled center ring set. Contraction of 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 26 orbital connections on doubled center ring set. Contraction of OJ12-2. Ring size specific.
Celtic
Rosette (5)
Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Sample Ring Count Note
Celtic Rosette 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.
Celtic Rosette 4
(M.A.I.L.)
Japanese, Orbital 2  5.5 5.5 +2= 8 Directional swirl of 4 basic orbital connections with each orbiting off the last orbital ring.
Celtic Rosette 5
(M.A.I.L.)
Japanese, Orbital 2 single: 5.65.7 5.7 +2= 10 Directional swirl of 5 basic orbital connections with each orbiting off the last orbital ring.
Celtic Rosette 6
(M.A.I.L.)
Japanese, Orbital 2 Single: 6.06.0 - 6.2 6.0 +2= 12 Directional swirl of 6 basic orbital connections with each orbiting off the last orbital ring.
Celtic Rosette 7 Japanese, Orbital 2  6.3+ 6.3 +2= 14 Directional swirl of 7 basic orbital connections with each orbiting off the last orbital ring.
OHC/OSC
(4)
NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing CountNote
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 CageContraction of OHC. Medium corner, small inner, large orbital rings.
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 CageContraction of COHC. Large corner, small cage + captive, large orbital rings.
Orbital Square Cage Unit (OSCU) Japanese, Orbital 3 single: 6.5single: 6.5+ 6.5 16
Orbital Square CageContraction of OSC, OSCWeb.
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 WebContraction of COSC, COSCWeb. Large captive ring.
Hourglass
(6)+
Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Sample Ring Count Note
Hourglass Unit
(M.A.I.L.)
Japanese, Orbital 3 single: ~6.66.6+ 7.0
(four units)
8 Folds inside out > 6.9 AR. Pentagonally tessellates as Hourglass Dodecahedron. Tutorial, 2.
Hourglass Unit (2) Japanese, Orbital 3 single: 6.76.7+ 6.7 +2= 10
Orbital Square CageHourglass Unit with 2 rings in each of 2 horizontal sets. Contraction of OHCWeb, OSC. Expands into Hourglass Hex (2). Pentagonally tessellates as Hourglass Dodecahedron (2). Tutorial, 2.
Hourglass Unit (3) Japanese, Orbital 4 single: 7.07.0+ 7.0 +2= 12
Hourglass Unit 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 +2= 14 Hourglass Unit 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 (6*6)=
36
Hourglass Unit repeated into a 6-sided unit. AR-sensitive.
Hourglass Hex (2) Japanese, Orbital 5 single: 7.17.2 - ~7.5 7.3 +6= 42
Orbital Hex Cage Web (Hourglass Web)Contraction of OHCWeb. Hourglass Unit (2) repeated into a 6-sided unit. AR-sensitive.
Missing
(3)
NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing CountNote
Missing Half An Hour Unit Japanese, Orbital 5 single: 6.86.8+ 6.8 16 Contraction of 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 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 Missing Half An Hour Square Sheet (2).
Tao/Not Tao
(10)
NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing CountNote
Tao 3
(M.A.I.L.)**
Japanese, Orbital, Reinforced 3  -(4.3, 5.5)+ 4.3, 5.5 8
Tao 3 SheetContraction of Tao 3 Sheet. **M.A.I.L. entry is multiple units bolted together in a chain sequence. Tutorial.
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 3 (NT3)
(M.A.I.L.)
Japanese, Reinforced 3  -(4.2, 5.5)+
-(3.2, 5.6, 6.7)+
3.2, 5.6, 6.7
4.2, 5.5
8
Not Tao 3 Sheet6-cell 2-1C hoop with reinforced rings on each side. Expands into NT3S. Repeats into NT3Web. Related to Upanishad Unit. Tutorial, 2.Not Tao 3 Web
Not Tao 4 (NT4)
(M.A.I.L.)
Japanese, Reinforced 3  -(3.4, 9.0, 7.0)+ 3.4, 9.0, 7.0
2WD
+2= 10 8-cell 2-1C hoop with reinforced rings on each side. 4-sided NT3.
Not Tao 5 (NT5)
(M.A.I.L.)
Japanese, Reinforced 3 N/AN/A 2WD** +2= 12 10-cell 2-1C hoop with reinforced rings on each side. 5-sided NT3. **2WD: .048" 13/64", .062" 1/2", 9/32". Tutorial.
Not Tao 6 (NT6)
(M.A.I.L.)
Japanese, Reinforced 3 N/AN/A 2WD** +2= 14 12-cell 2-1C hoop with reinforced rings on each side. 6-sided NT3. **2WD: .062" .602" (MD), .048" 13/64", .062" 9/32". Tutorial.
Not Tao 7 (NT7) Japanese, Reinforced 3 N/AN/A 2WD** +2= 16 14-cell 2-1C hoop with reinforced rings on each side. 7-sided NT3. **2WD: .062" .708" (MD), .048" 13/64", .062" 9/32".
Not Tao 8 (NT8) Japanese, Reinforced 3 N/AN/A 2WD** +2= 18 16-cell 2-1C hoop with reinforced rings on each side. 8-sided NT3. **2WD: .062" .708" (MD), .048" 13/64", .062" 29/128".
Not Tao 9 (NT9) Japanese, Reinforced 3 N/AN/A 3WD** +2= 20 18-cell 2-1C hoop with reinforced rings on each side. 9-sided NT3. **3WD: .080" .850" (MD), .048" 15/64", .062" 7/32".
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 SheetContraction of NT3S. Related to NT3. Ring size specific.
Borealis / Celtic Visions (7)+NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing Count
BorealisBorealis / CelticCeltic / Celtic VisionsCV-based.
Inverted Aura
(M.A.I.L.)
Japanese 3 3.0, >5.63.0, -6.0+ 3.0, 6.0 11 Contraction of Borealis, Helm Chain Web.
Aura Unit
(M.A.I.L.)**
Japanese 3  - 3.0, 5.6 13
Celtic WebContraction of Borealis, CWeb, CV Dodecahedron. Completely unstable as a standalone: collapses inward. **M.A.I.L. entry is multiple units bolted together in chain sequence.Celtic Visions Dodecahedron
Celtic Circle 3 (CC3)
(M.A.I.L.)
Japanese 4  -3.3, -8.3+
2WD
3.3, 8.3 (3*7)=
21
3-cell Celtic chain hoop. Contraction of Borealis. a.k.a. "Borealis Unit".
Celtic Circle 4 (CC4) Japanese 4 3.0, >5.1-(3.1, 5.5)+ 3.1, 5.5 (4*7)=
28
4-cell Celtic chain hoop.
Celtic Circle 5 (CC5) Japanese 4  -(3.1, 5.1)+ 3.1, 5.1 (5*7)=
35
5-cell Celtic chain hoop.
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
4-cell CV chain hoop.
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
5-cell CV chain hoop. Adding corner rings produces CVC5Star.Celtic Visions Circle 5 Star
Byzantine
(4)+
Name Family/Sub Ring
Type
Minimum AR Ideal AR1 group Ring Count
ByzantineByzantine-based.
Byzantine 3 Unit (Byz3U) European 3    3.3, 4.0 (3*6+2)=
20
Byzantine Web3 Byz cells off central doubled ring set. Contraction of Byz Web.
Byzantine 4 Unit (Byz4U) European 3    3.3, 5.4 (4*6+2)=
26
Byzantine Web Square4 Byz cells off central doubled ring set. Contraction of Byz Web Square.
Byzantine 5 Unit (Byz5U) European 3    3.3, 7.0 (5*6+2)=
32
5 Byz cells off central doubled ring set. Pentagonally tessellates as Byz Dodecahedron.Byzantine Dodecahedron
Byzantine 6 Unit (Byz6U) European 3    3.2, 8.5 (6*6+2)=
38
Byzantine Web Triangle6 Byz cells off central doubled ring set. Contraction of Byz Web Triangle.
B3/B2
(2)
NameFamily/SubRing
Type
Minimum ARIdeal AR1SampleRing CountNote
B
(M.A.I.L.)**
Japanese, European 4 >4.4-4.7 4.7 (3*8)=
24
Repeats into B Web. **M.A.I.L. entry has inside set of rings singled.B Web
B+1
(M.A.I.L.)
Japanese, European 4 4.44.4 4.4 (4*8+1)=
33
B unit with an extra ring in the middle for structure. Ideal for chess kings. Tutorial.
3D
(18)
Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Samples Ring Count Note
Orb
(13)
               
Tetra Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Samples Ring Count
Repeats into Tetra Orb Cube.Tetra Orb Cube (2)
Tetra Orb
(M.A.I.L.)
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 +6= 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 +6= 28 Triple protruding rings. Tutorial.
Johnson Solid Steel Balls Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Samples Ring Count Note
Johnson Solid Steel Balls
(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 Balls (2) Japanese, Orbital 3 single: 6.86.8 - 7.0+ 6.8
(2)
+9= 33 Double protruding rings.
Johnson Solid Steel Balls (3) Japanese, Orbital 4 single 7.37.3+ 7.3
(2)
+9= 42 Triple protruding rings.
Octa Name Family/Sub Ring
Type
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)
+12= 44 Double protruding rings.
Octa Orb (3) Japanese, Orbital 4  7.8+ 7.8 +12= 56 Triple protruding rings.
Hexa Name Family/Sub Ring
Type
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)
+12= 42 Double protruding rings. Sample is a bit loose.
Hexa Orb (3) Japanese, Orbital 4    11, 7.0, 5.9, 5.7
(2) (3)
+12= 54 Triple protruding rings.
Dodeca Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Samples Ring Count Note
Dodeca Orb (2) Japanese, Orbital 3    13, 7.0, 5.9
(2)
(12+30*2+30)=
102
12-ring dodecahedron core. 30 edges each have an orbital ring held in place by protruding rings, doubled.
Dodecahedron (5) Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Sample Ring Count Note
Hourglass Dodecahedron Japanese, Orbital 3 single: 6.9 or 7.06.9? - 7.0 7.0 140
Hourglass UnitHourglass Units with pentagonal tessellation forced into a sphere. Tutorial.
Hourglass Dodecahedron (2)
(M.A.I.L.)
Japanese, Orbital 3 single: 7.17.1 - 7.2 7.4, 7.3, 6.6
7.1
+20= 160
Hourglass Unit (2)Double center rings. Related to OHC, OHCWeb. Hourglass Unit (2) with pentagonal tessellation forced into a sphere. Tutorial.
Hourglass Dodecahedron (3) Japanese, Orbital 4 single: 7.77.7+ 7.7 +20= 180
Hourglass Unit (3)Triple center rings. Hourglass Unit (3) with pentagonal tessellation forced into a sphere. Tutorial.
Celtic Visions Dodecahedron
(M.A.I.L.)
Japanese 6  2WD 2WD
(2)
242
Celtic VisionsCV segments/Aura Units repeated into a sphere. a.k.a. "Celtic Rose Sheet (Pentagonal Tessellation)".Aura Unit
Byzantine Dodecahedron European 4  3.3, 7.2 3.3, 7.2 10*30 + 2*12= 324
Byzantine10-ring Byz segments tessellated pentagonally as Byz5U, continued into a sphere.Byzantine 5 Unit
Mobius
(9)
Name Family/Sub Ring
Type
Minimum AR Ideal AR1 Sample Ring Count
Related to Spiral weaves.Spiral 4 in 1 Web
Mobius Ball
(M.A.I.L.)
Spiral 1 N/A-6.0 - 14.0+ 14 Variable Sphere composed of several rings of the same size, each passing through every other ring and leaning in the same direction. Tutorial.
Mobius 3 Spiral 1 2.02.1+ table 3
Base construct of Voodoo Hex. This "unit" sometimes replaces single rings. Voodoo Hex
Mobius 4 Spiral 1 2.4 or 2.52.5+ table 4
Spiral 4 in 1 Spiral 4 in 1 basis. Base construct of Hoodoo (Sheet), Voodoo. Repeats into Brejao Flowers. Hoodoo (Sheet)
Mobius 5 Spiral 1 3.03.1+ table 5 Five ring mobius.
Mobius 6 Spiral 1 3.23.3+ table 6
Spiral 6 in 1Spiral 6 in 1, Moorish Rose basis.
Mobius 7 Spiral 1 3.6 or 3.73.7+ table 7 Seven ring mobius.
Mobius 8 Spiral 1 3.94.0+ table 8
Spiral 8 in 1Spiral 8 in 1 basis.
Mobius 9 Spiral 1 4.24.3+ table 9 Nine ring mobius.
Mobius 10 Spiral 1 4.5 or 4.64.6+ table 10 Ten ring mobius.


OJ | Celtic Rosette | OHC/OSC | OS/IOS
Hourglass | Missing | Tao/Not Tao
Borealis/Celtic/CV | Byz | B3/B2
Tetra Orb | Dodecahedron
Mobius



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.



Other resources:

M.A.I.L. Weave Library - Units
M.A.I.L. Weave Library - 3D Weaves