Hsin-Po's Website

Oriclip

One of my interests involves building binder clip sculptures. The name oriclip is inspired by origami, which stands for ori “fold” and kami “paper”. Note that binder clips are sometimes called foldover clip or foldback clip.

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(The page is under construction; check back periodically.)

Special case

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

6-clip constructions

6-cycle

6 binder clips forming a cycle
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6

6-dense

6 binder clips clipping and interlocking densely
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6

6-wedge

6 binder clips with mouths pointing outward
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12

6-fitin

6 binder clips with handles fit in notches
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12

6-twist

6 binder clips with interlocking handles
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12

6-cross

6 binder clips forming a 3D cross
↑ # Clips = 6
↑ Base = three-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24

6-spike

6 binder clips with spiky handles
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24

6-stand

6 binder clips whose bodies stand on the octahedron formed by handles
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24

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 = $S_4$ of order 24

S30-aD

30 clips forming icosidodecahedron
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

A-series

One clip = one edge.

A12-O

12 clips forming spiky octahedron
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24

A24-aC

24 clips forming spiky cuboctahedron
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24

A36-kC

36 clips forming spiky tetrakis hexahedron
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24

A48-aaC

48 clips forming spiky rhombicuboctahedron
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24

Vertex unit

Φ-series

Three clips = one Φ-vertex = one vertex.

Φ24-C

24 clips forming 12 Φ-edges forming cube
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24-O

Φ24-O

24 clips forming 12 Φ-edges forming octahedron
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24-C

Δ-series

Three clips = one Δ-vertex = one vertex.

Δ60-D

60 clips forming 30 Δ-edges forming dodecahedron
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

Δ180-tI

60 clips forming 30 Δ-edges forming truncated icosahedron
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

Edge unit

X-series

Two clips = one X-edge = one edge.

X12-T

12 clips forming 6 X-edges forming tetrahedron
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself

X24-C

24 clips forming 12 X-edges forming cube
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ dual = X24-C

X60-D

60 clips forming 30 X-edges forming dodecahedron
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60-I

X60-I

60 clips forming 30 X-edges forming icosahedron
↑ # Clips = 30
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60-D

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 = $A_4$ of order 12
↑ 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 = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ Dual = L24-C

L60-D

60 clips forming 30 L-edges forming dodecahedron
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_4$ of order 12

L48-aC

48 clips forming 24 L-edges forming cuboctahedron
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24

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 = $A_4$ of order 12
↑ 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 = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ 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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ dual = I60-D

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 = $A_4$ of order 12
↑ 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 = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ (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 = $S_4$ of order 24
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 = $S_4$ of order 24
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 = $S_4$ of order 24
↑ (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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60

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 = $A_5$ of order 60
↑ (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 = $A_4$ of order 12
↑ 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 = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_4$ of order 12
↑ Dual = itself

W24-C

24 clips forming 12 W-edges forming cube
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ 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 = $S_4$ of order 24
↑ dual = W24-C

W60-D

60 clips forming 30 W-edges forming dodecahedron
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ 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 = $A_5$ of order 60
↑ 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 = $A_4$ of order 12

W120-aD

120 clips forming 60 W-edges forming icosidodecahedron
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

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 my naming scheme, see Conway notation and list of “G” polyhedra. Or play with this interactive web app: polyHédronisme. (Refresh to get random example!)

Similar clip works by other people

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