HsinPo'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.
Fast scroll to
 Special case: 2clip, 6clip, polylink, Sseries, Aseries
 Vertex unit: Φseries, Δseries
 Edge unit: Xseries, Lseries, IPlatonic, IArchimedean, ICatalan, IFullerene, Wseries
(The page is under construction; check back periodically.)
Special case
2clip constructions
2ftf
↑ # Clips = 2
2btb
↑ # Clips = 2
6clip constructions
6cycle
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6
6dense
↑ # Clips = 6
↑ Base = sixpiece burr
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6
6wedge
↑ # Clips = 6
↑ Base = sixpiece burr
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
6fitin
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
6twist
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
6cross
↑ # Clips = 6
↑ Base = threepiece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
6spike
↑ # Clips = 6
↑ Base = sixpiece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
6stand
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
Polylink
Q12aC
↑ # Clips = 12
↑ Base = cuboctahedron
Sseries
One clip = one vertex. One handle = one edge.
S12aC
↑ # Clips = 12
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
S30aD
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
Aseries
One clip = one edge.
A12O
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
A24aC
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
A36kC
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
A48aaC
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
Vertex unit
Φseries
Three clips = one Φvertex = one vertex.
Φ24C
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24O
Φ24O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24C
Δseries
Three clips = one Δvertex = one vertex.
Δ60D
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
Δ180tI
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
Edge unit
Xseries
Two clips = one Xedge = one edge.
X12T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
X24C
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = X24O
X24O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = X24C
X60D
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60I
X60I
↑ # Clips = 30
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60D
Lseries
Two clips = one Ledge = one edge.
L12T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
L24C
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = L24O
L24O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = L24C
L60D
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = L60I
L60I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = L60D
L36tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
L48aC
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
Iseries, Platonic
Two clips = one Iedge = one edge.
I12T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
I24C
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = I24O
I24O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I24C
I60D
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I60I
I60I
↑ # Clips = 30
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = I60D
Iseries, Archimedean
I36tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = I36kT
I48aC
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I48jC
I72tC
↑ # Clips = 72
↑ Base = truncated cube
↑ Vertex config = 3.8.8
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = triakis octahedron)
I72tO
↑ # Clips = 72
↑ Base = truncated octahedron
↑ Vertex config = 4.6.6
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ I72kC
I96aaC
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ I96jjC
I120sC
↑ # Clips = 120
↑ Base = snub cube
↑ Vertex config = 3.3.3.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = pentagonal icositetrahedron)
I120aD
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I120jD
I180tI
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.5.6
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I180kD
I240aaD
↑ # Clips = 240
↑ Base = rhombicosidodecahedron
↑ Vertex config = 3.4.5.4
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
I300sD
↑ # Clips = 300
↑ Base = snub dodecahedron
↑ Face config = 3.3.3.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ (Dual = pentagonal hexecontahedron)
Iseries, Catalan
I36kT
↑ # Clips = 36
↑ Face config = 3.6.6
↑ Base = triakis tetrahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = I36tT
I48jC
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I48aC
I72kC
↑ # Clips = 72
↑ Base = tetrakis hexahedron
↑ Face config = 4.6.6
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I72tO
I96jjC
↑ # Clips = 96
↑ Base = deltoidal icositetrahedron
↑ Face config = 3.4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ I96aaC
I120jD
↑ # Clips = 120
↑ Base = rhombic triacontahedron
↑ Face config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I120aD
I180kD
↑ # Clips = 120
↑ Base = pentakis dodecahedron
↑ Face config = 5.6.6
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I180tI
Iseries, Fullerene
I240cD
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I240uI
I240uI
↑ # Clips = 240
↑ Base = pentakis icosidodecahedron aka C80
↑ Each icosahedron face = 4 small triangles
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I240cD
Wseries
W12T
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
W24C
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = W24O
W24O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = W24C
W60D
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = W60I
W60I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = W60D
W36tT
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
W120aD
↑ # 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

http://zacharyabel.com/sculpture/ by Zachary Abel.

https://www.instructables.com/BinderClipBall/ by 69valentine.

http://blog.andreahawksley.com/tag/binderclips/ by Andrea Hawksley.