Postdoc @ UC San Diego
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.
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↑ # Clips = 2
↑ # Clips = 2
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = triangular antiprism’s rotations
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 6
↑ Base = three-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 12
↑ Base = cuboctahedron
One clip = one vertex. One handle = one edge.
↑ # Clips = 12
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations
One clip = one edge.
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations
↑ # Clips = 60
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ # Clips = 96
↑ Local base = octahedron
↑ Global base = cube
↑ Symmetry = cube’s rotations
↑ # Clips = 144
↑ Local base = cuboctahedron
↑ Global base = octahedron
↑ Symmetry = cube’s rotations
Four clips = one Η-vertex = one vertex.
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ # Clips = 120
↑ Base = application of the loft operation upon a cube
↑ Symmetry = cube’s rotations
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 48
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = pyritohedron’s rotations and reflections
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
↑ # Clips = 48
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = tetrahedron’s rotations
Three clips = one Φ-vertex = one vertex.
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = Φ24-C
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
Three clips = one Δ-vertex = one vertex.
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations
Three clips = one Y-edge = one edge.
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
Two clips = one X-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = X24-O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = X24-C
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-I
↑ # Clips = 60
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations
↑ dual = X60-D
↑ # Clips = 120
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
Two clips = one L-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ Dual = L24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = L24-C
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = L60-D
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.6.6
↑ Symmetry = dodecahedron’s rotations
Two clips = one I-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = I24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ Dual = I24-C
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I60-I
↑ # Clips = 30
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ dual = I60-D
↑ # Clips = 24
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-kT
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-jC
↑ # Clips = 72
↑ Base = truncated cube
↑ Vertex config = 3.8.8
↑ Symmetry = cube’s rotations
↑ (Dual = triakis octahedron)
↑ # Clips = 72
↑ Base = truncated octahedron
↑ Vertex config = 4.6.6
↑ Symmetry = cube’s rotations
↑ I72-kC
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-jjC
↑ # Clips = 120
↑ Base = snub cube
↑ Vertex config = 3.3.3.3.4
↑ Symmetry = cube’s rotations
↑ (Dual = pentagonal icositetrahedron)
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-jD
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.5.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-kD
↑ # Clips = 240
↑ Base = rhombicosidodecahedron
↑ Vertex config = 3.4.5.4
↑ Symmetry = dodecahedron’s rotations
↑ # Clips = 300
↑ Base = snub dodecahedron
↑ Face config = 3.3.3.3.5
↑ Symmetry = dodecahedron’s rotations
↑ (Dual = pentagonal hexecontahedron)
↑ # Clips = 36
↑ Face config = 3.6.6
↑ Base = triakis tetrahedron
↑ Symmetry = tetrahedron’s rotations
↑ Dual = I36-tT
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations
↑ Dual = I48-aC
↑ # Clips = 72
↑ Base = tetrakis hexahedron
↑ Face config = 4.6.6
↑ Symmetry = cube’s rotations
↑ Dual = I72-tO
↑ # Clips = 96
↑ Base = deltoidal icositetrahedron
↑ Face config = 3.4.4.4
↑ Symmetry = cube’s rotations
↑ I96-aaC
↑ # Clips = 120
↑ Base = rhombic triacontahedron
↑ Face config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I120-aD
↑ # Clips = 120
↑ Base = pentakis dodecahedron
↑ Face config = 5.6.6
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I180-tI
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-uI
↑ # Clips = 240
↑ Base = pentakis icosidodecahedron aka C80
↑ Each icosahedron face = 4 small triangles
↑ Symmetry = dodecahedron’s rotations
↑ Dual = I240-cD
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations
↑ Dual = itself
Difficulty encountered
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations
↑ dual = W24-O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations
↑ dual = W24-C
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations
↑ Dual = W60-D
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations
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 works have been published under the names binder clip sculpture and binder clip ball.
http://zacharyabel.com/sculpture/ by Zachary Abel.
https://www.instructables.com/Binder-Clip-Ball/ by 69valentine.
http://blog.andreahawksley.com/tag/binderclips/ by Andrea Hawksley.
https://binderclippolyhedra.com/ by unknown author.
https://momath.org/mathmonday/math-monday-what-to-make-from-binder-clips/ a news article by George Hart.
https://www.rocky-lau.com/ LEGO counterpart by Rocky Lau.