Hsin-Po's Website
Modular 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”. Sometimes, binder clips are called foldover clip or foldback clip.
Fast scroll to
- Special case: 2-clip, 6-clip, 12-clip, polylink, S-series, A-series
- Vertex unit: Η-series, Φ-series, Ψ-series, Δ-series
- Edge unit: Y-series, X-series, L-series, I-Platonic, I-Archimedean, I-Catalan, I-Fullerene, W-series
Special case
2-clip constructions
2-ftf
↑ # Clips = 2
2-btb
↑ # Clips = 2
2-hth
↑ # Clips = 2
6-clip constructions
6-cycle
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations
6-dense
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = triangular antiprism’s rotations
6-wedge
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = tetrahedron’s rotations
6-fitin
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations
6-twist
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations
6-cross
↑ # Clips = 6
↑ Base = three-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections
6-spike
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections
6-stand
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
12-clip constructions
12-angel
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
Polylink
Q12-aC
↑ # Clips = 12
↑ Base = cuboctahedron
S-series
One clip = one vertex. One handle = one edge.
S12-aC
↑ # Clips = 12
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations
S30-aD
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations
A-series
One clip = one edge.
A12-O
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
A24-aC
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations
A36-kC
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections
A48-aaC
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations
A60-aD*
↑ # Clips = 60
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations
A12-O8-C
↑ # Clips = 96
↑ Local base = octahedron
↑ Global base = cube
↑ Symmetry = cube’s rotations
A24-aC4-T
↑ # Clips = 96
↑ Local base = cuboctahedron
↑ Global base = tetrahedron
↑ Symmetry = tetrahedron’s rotations
A24-aC8-O
↑ # Clips = 144
↑ Local base = cuboctahedron
↑ Global base = octahedron
↑ Symmetry = cube’s rotations
Vertex unit
Η-series
Four clips = one Η-vertex = one vertex.
Η24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections
Η48-jC
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations
Η120-aD
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations
Η120-lC
↑ # Clips = 120
↑ Base = application of the loft operation upon a cube
↑ Symmetry = cube’s rotations
Η24-T
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
Η48-O
↑ # Clips = 48
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections
Η48-C
↑ # 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.
↑ # 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.
↑ # Clips = 120
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
Φ-series
Three clips = one Φ-vertex = one vertex.
Φ12-T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
Φ24-C
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-O
Φ24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-C
ΦB60-I
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations
ΦJ60-D
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
Ψ-series
Three clips = one Ψ-vertex = one vertex.
Ψ12-T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
Ψ24-C
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = Ψ24-O
Ψ24-O
↑ # 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
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
Δ180-tI
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations
Edge unit
Y-series
Three clips = one Y-edge = one edge.
Y18-T
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
X-series
Two clips = one X-edge = one edge.
X12-T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
X24-C
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = X24-O
X24-O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = X24-C
X60-D
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-I
X60-I
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-D
XX120-D
↑ # Clips = 120
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
L-series
Two clips = one L-edge = one edge.
L12-T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
L24-C
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = L24-O
L24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = L24-C
L60-D
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-I
L60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-D
L36-tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
L48-aC
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations
L180-tI
↑ # 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
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
I24-C
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = I24-O
I24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = I24-C
I60-D
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I60-I
I60-I
↑ # Clips = 30
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ dual = I60-D
II24-T
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
I-series, Archimedean
I36-tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-kT
I48-aC
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-jC
I72-tC
↑ # Clips = 72
↑ Base = truncated cube
↑ Vertex config = 3.8.8
↑ Symmetry = cube’s rotations
↑ (Dual = triakis octahedron)
I72-tO
↑ # Clips = 72
↑ Base = truncated octahedron
↑ Vertex config = 4.6.6
↑ Symmetry = cube’s rotations
↑ I72-kC
I96-aaC
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-jjC
I120-sC
↑ # Clips = 120
↑ Base = snub cube
↑ Vertex config = 3.3.3.3.4
↑ Symmetry = cube’s rotations
↑ (Dual = pentagonal icositetrahedron)
I120-aD
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-jD
I180-tI
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.5.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-kD
I240-aaD
↑ # Clips = 240
↑ Base = rhombicosidodecahedron
↑ Vertex config = 3.4.5.4
↑ Symmetry = dodecahedron’s rotations
I300-sD
↑ # Clips = 300
↑ Base = snub dodecahedron
↑ Face config = 3.3.3.3.5
↑ Symmetry = dodecahedron’s rotations
↑ (Dual = pentagonal hexecontahedron)
I-series, Catalan
I36-kT
↑ # Clips = 36
↑ Face config = 3.6.6
↑ Base = triakis tetrahedron
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-tT
I48-jC
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-aC
I72-kC
↑ # Clips = 72
↑ Base = tetrakis hexahedron
↑ Face config = 4.6.6
↑ Symmetry = cube’s rotations
↑ Dual = I72-tO
I96-jjC
↑ # Clips = 96
↑ Base = deltoidal icositetrahedron
↑ Face config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-aaC
I120-jD
↑ # Clips = 120
↑ Base = rhombic triacontahedron
↑ Face config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-aD
I180-kD
↑ # Clips = 120
↑ Base = pentakis dodecahedron
↑ Face config = 5.6.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-tI
I-series, Fullerene
I240-cD
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-uI
I240-uI
↑ # Clips = 240
↑ Base = pentakis icosidodecahedron aka C80
↑ Each icosahedron face = 4 small triangles
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-cD
W-series
W12-T
↑ # 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
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = W24-C
W60-D
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-I
W60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-D
W36-tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
W120-aD
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
W240-cD
↑ # 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 “G” polyhedra. Or play with this interactive web app: polyHédronisme. (Refresh to get random example!)
Similar clip works by other people
Similar works have been published under the names binder clip sculpture and binder clip ball.
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http://zacharyabel.com/sculpture/ by Zachary Abel.
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https://www.instructables.com/Binder-Clip-Ball/ by 69valentine.
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http://blog.andreahawksley.com/tag/binderclips/ by Andrea Hawksley.
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https://binderclippolyhedra.com/ by unknown author.
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https://momath.org/mathmonday/math-monday-what-to-make-from-binder-clips/ a news article by George Hart.
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https://www.rocky-lau.com/ LEGO counterpart by Rocky Lau.