Hsin-Po Wang's Website

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Fellow @ Simons Institute

Modular Oriclip

I am enthusiastic about building binder clip sculptures. I made up the name oriclip, which is inspired by my older habit origami, which stands for ori “fold” and kami “paper”.

(In some places, UK and its friends I suppose, binder clips are called foldover clips or foldback clips, which sort-of justifies the prefix ori.)

Fast forward to

Special cases

2-clip constructions

2-ftf

2 binder clips touch face to face
↑ # Clips = 2

2-btb

2 binder clips hold back to back
↑ # Clips = 2

2-hth

2 binder clips hold hand to hand
↑ # Clips = 2

6-clip constructions

6-cycle

6 binder clips forming a cycle
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations

6-dense

6 binder clips clipping and interlocking densely
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = triangular antiprism’s rotations

6-wedge

6 binder clips with mouths pointing outward
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = tetrahedron’s rotations

6-fitin

6 binder clips with handles fit in notches
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations
↑ Video instruction = https://youtu.be/XCLxfR3sDGM

6-twist

6 binder clips with interlocking handles
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations

6-cross

6 binder clips forming a 3D cross
↑ # Clips = 6
↑ Base = three-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections
↑ Video instruction = https://youtu.be/8F8225Ve_RE
↑ Looks like = Czech hedgehog

6-spike

6 binder clips with spiky handles
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections

6-stand

6 binder clips whose bodies stand on the octahedron formed by handles
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections

12-clip construction

12-angel

6 binder clips form an octahedron, another 6 form tentacles ↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections

Q12-aC

12 binder clips forming 4 triangles forming a polylink
↑ # Clips = 12
↑ Base = cuboctahedron

S-series

One clip = one vertex. One handle = one edge.

S12-aC

12 clips forming cuboctahedron
↑ # Clips = 12
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations

S30-aD

30 clips forming icosidodecahedron
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations

A-series

One clip = one edge.

A12-O

12 clips forming spiky octahedron
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
↑ Video instruction = https://youtu.be/aXINnqdEPB8
↑ Looks like = Ramiel in Evangelion

A24-aC

24 clips forming spiky cuboctahedron
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations

A36-kC

36 clips forming spiky tetrakis hexahedron
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections

A48-aaC

48 clips forming spiky rhombicuboctahedron
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations

A60-aD*

60 clips forming icosidodecahedron, but with helps
↑ # Clips = 60
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations

A12-O8-C

12 clips forming spiky octahedron, 8 of that forming cube
↑ # Clips = (12 per vertex) x (8 vertices) = 96
↑ Local base = octahedron
↑ Global base = cube
↑ Symmetry = cube’s rotations

A24-aC4-T

24 clips forming spiky cuboctahedron, 4 of that forming tetrahedron
↑ # Clips = (24 per vertex) x (4 vertices) = 96
↑ Local base = cuboctahedron
↑ Global base = tetrahedron
↑ Symmetry = tetrahedron’s rotations

A24-aC8-O

24 clips forming spiky cuboctahedron, 6 of that forming octahedron
↑ # Clips = (24 per vertex) x (8 vertices) = 144
↑ Local base = cuboctahedron
↑ Global base = octahedron
↑ Symmetry = cube’s rotations

Vertex units

Η-series

Four clips = one Η-vertex = one vertex.

Η24-O

24 clips forming 6 Η-vertices forming octahedron
↑ # Clips = (4 per face) x (6 faces) = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections
↑ Video instruction = https://youtu.be/Crru2VOmpL4

Η48-jC

48 clips forming 12 Η-vertices forming rhombic dodecahedron
↑ # Clips = (4 per vertex) x (12 vertices) = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations

Η120-aD

120 clips forming 30 Η-vertices forming icosidodecahedron ↑ # Clips = (4 per face) x (30 vertices) = 120
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations

Η120-lC

24 clips forming 30 Η-faces forming lofted cube
↑ # Clips = 120
↑ Base = application of the loft operation upon a cube
↑ Symmetry = cube’s rotations

Η24-T

24 clips forming 4 Η-vertices forming tetrahedron
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations

Η48-O

48 clips forming 6 Η-vertices forming octahedron
↑ # Clips = 48
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections

Η48-C

48 clips forming 8 Η-vertices forming cube
↑ # Clips = 48
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = tetrahedron’s rotations

H48-O

This “H” is the Latin Ech because it is used as an edge unit. The other “Η” are Greek Eta because they are used as vertex unit.

48 clips forming 12 H-edges forming octahedron
↑ # Clips = 48
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations

H120-D

This “H” is the Latin Ech because it is used as an edge unit. The other “Η” are Greek Eta because they are used as vertex unit.

120 clips forming 30 H-edges forming dodecahedron
↑ # Clips = 120
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations

Φ-series

Three clips = one Φ-vertex = one vertex.

Φ12-T

12 clips forming 4 Φ-vertices forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

Φ24-C

24 clips forming 8 Φ-vertices forming cube
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-O

Φ24-O

24 clips forming 6 Φ-vertices forming octahedron
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-C

ΦB60-I

60 clips forming 12 Φ-vertices and 30 B-edges forming Icosahedron
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations

ΦJ60-D

60 clips forming 20 Φ-vertices and 30 J-edges forming Dodecahedron
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations

Ψ-series

Three clips = one Ψ-vertex = one vertex.

Ψ12-T

12 clips forming 4 Ψ-vertices forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

Ψ24-C

24 clips forming 8 Ψ-vertices forming cube
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = Ψ24-O

Ψ24-O

24 clips forming 6 Ψ-vertices forming octahedron
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = Ψ24-C

Δ-series

Three clips = one Δ-vertex = one vertex.

Δ60-D

60 clips forming 30 Δ-vertices forming dodecahedron
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations

Δ180-tI

60 clips forming 30 Δ-vertices forming truncated icosahedron
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations

Edge units

Y-series

Three clips = one Y-edge = one edge.

Y18-T

18 clips forming 6 Η-edges forming tetrahedron
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations

X-series

Two clips = one X-edge = one edge.

X12-T

12 clips forming 6 X-edges forming tetrahedron
↑ # Clips = (2 per edge) x (6 edges) = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
↑ Video Instruction = https://youtu.be/0hu1LEuSWS4
↑ Looks like = Roman sueface

X24-C

24 clips forming 12 X-edges forming cube
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = X24-O

X24-O

24 clips forming 12 X-edges forming octahedron
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = X24-C

X60-D

60 clips forming 30 X-edges forming dodecahedron
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-I

X60-I

60 clips forming 30 X-edges forming icosahedron
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-D

XX120-D

120 clips forming 30 XX-edges forming dodecahedron
↑ # Clips = 120
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations

L-series

Two clips = one L-edge = one edge.

L12-T

12 clips forming 6 L-edges forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

L24-C

24 clips forming 12 L-edges forming cube
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = L24-O

L24-O

24 clips forming 12 L-edges forming octahedron
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = L24-C
↑ Video instruction = https://youtu.be/rpFVjyZ3XF8
↑ Looks like = gyroscope frame

L60-D

60 clips forming 30 L-edges forming dodecahedron
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-I

L60-I

60 clips forming 30 L-edges forming icosahedron
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-D

L36-tT

36 clips forming 18 L-edges forming truncated tetrahedron
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations

L48-aC

48 clips forming 24 L-edges forming cuboctahedron
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations

L180-tI

180 clips forming 90 L-edges forming truncated icosahedron
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.6.6
↑ Symmetry = dodecahedron’s rotations

I-series, Platonic

Two clips = one I-edge = one edge.

I12-T

12 clips forming 6 I-edges forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

I24-C

24 clips forming 12 I-edges forming cube
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = I24-O

I24-O

24 clips forming 12 I-edges forming octahedron
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = I24-C

I60-D

60 clips forming 30 I-edges forming dodecahedron
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I60-I

I60-I

60 clips forming 30 I-edges forming icosahedron
↑ # Clips = 30
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ dual = I60-D

II24-T

24 clips forming 6 II-edges forming tetrahedron
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

I-series, Archimedean

I36-tT

36 clips forming 18 I-edges forming truncated tetrahedron
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-kT

I48-aC

48 clips forming 24 I-edges forming cuboctahedron
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-jC

I72-tC

72 clips forming 36 I-edges forming truncated cube
↑ # Clips = 72
↑ Base = truncated cube
↑ Vertex config = 3.8.8
↑ Symmetry = cube’s rotations
↑ (Dual = triakis octahedron)

I72-tO

72 clips forming 36 I-edges forming truncated octahedron
↑ # Clips = 72
↑ Base = truncated octahedron
↑ Vertex config = 4.6.6
↑ Symmetry = cube’s rotations
↑ I72-kC

I96-aaC

96 clips forming 96 I-edges forming rhombicuboctahedron
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-jjC

I120-sC

120 clips forming 60 I-edges forming snub cube
↑ # Clips = 120
↑ Base = snub cube
↑ Vertex config = 3.3.3.3.4
↑ Symmetry = cube’s rotations
↑ (Dual = pentagonal icositetrahedron)

I120-aD

120 clips forming 60 I-edges forming icosidodecahedron
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-jD

I180-tI

180 clips forming 90 I-edges forming truncated icosahedron
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.5.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-kD

I240-aaD

240 clips forming 120 I-edges forming rhombicosidodecahedron
↑ # Clips = 240
↑ Base = rhombicosidodecahedron
↑ Vertex config = 3.4.5.4
↑ Symmetry = dodecahedron’s rotations

I300-sD

300 clips forming 150 I-edges forming snub dodecahedron
↑ # Clips = 300
↑ Base = snub dodecahedron
↑ Face config = 3.3.3.3.5
↑ Symmetry = dodecahedron’s rotations
↑ (Dual = pentagonal hexecontahedron)

I-series, Catalan

I36-kT

36 clips forming 18 I-edges forming triakis tetrahedron
↑ # Clips = 36
↑ Face config = 3.6.6
↑ Base = triakis tetrahedron
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-tT

I48-jC

48 clips forming 24 I-edges forming rhombic dodecahedron
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-aC

I72-kC

72 clips forming 36 I-edges forming tetrakis hexahedron
↑ # Clips = 72
↑ Base = tetrakis hexahedron
↑ Face config = 4.6.6
↑ Symmetry = cube’s rotations
↑ Dual = I72-tO

I96-jjC

96 clips forming 96 I-edges forming deltoidal icositetrahedron
↑ # Clips = 96
↑ Base = deltoidal icositetrahedron
↑ Face config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-aaC

I120-jD

120 clips forming 60 I-edges forming rhombic triacontahedron
↑ # Clips = 120
↑ Base = rhombic triacontahedron
↑ Face config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-aD

I180-kD

180 clips forming 90 I-edges forming pentakis dodecahedron
↑ # Clips = 120
↑ Base = pentakis dodecahedron
↑ Face config = 5.6.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-tI

I-series, Fullerene

I240-cD

240 clips forming 120 I-edges forming chamfered dodecahedron
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-uI

I240-uI

240 clips forming 120 I-edges forming pentakis icosidodecahedron
↑ # Clips = 240
↑ Base = pentakis icosidodecahedron aka C80
↑ Each icosahedron face = 4 small triangles
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-cD

W-series

W12-T

12 clips forming 6 W-edges forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself

W24-C

Difficulty encountered
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = W24-O

W24-O

24 clips forming 12 W-edges forming octahedron
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = W24-C

W48-aC

48 clips forming 24 W-edges forming cuboctahedron
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations

W60-D

60 clips forming 30 W-edges forming dodecahedron
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-I

W60-I

60 clips forming 30 W-edges forming icosahedron
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-D

W36-tT

36 clips forming 18 W-edges forming truncated tetrahedron
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations

W120-aD

120 clips forming 60 W-edges forming icosidodecahedron
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations

W240-cD

240 clips forming 60 W-edges forming chamfered dodecahedron
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations

Read more

For a systematic introduction of polyhedra, checkout Platonic solid and Archimedean solid and its dual Catalan solid and the references therein.

For more on symmetry groups, see Polyhedral group and the references therein.

For the naming scheme, see Conway notation and List_of_geodesic_polyhedra_and_Goldberg_polyhedra. Or play with this interactive web app: polyHédronisme. (Refresh the page to get random example!)

Thank You for Attention

vaseman and oriclip

Please email me if you have questions (perhaps you want to teach binder clip sculpture in a class) or contributions (when you make something not seen on this page). Once you have made sufficiently many sculptures, you might as well showcase them on a personal website. Notify me so I can put your link below.

Similar clip works by other people

Similar works have been published under the names binder clip sculpture and binder clip ball.