Math PhD @ UIUC
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.)
↑ # Clips = 2
↑ # Clips = 2
↑ # Clips = 6
↑ Base = triangular antiprism
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = triangular antiprism’s rotations = $D_6$ of order 6
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ # Clips = 6
↑ Base = three-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
↑ # Clips = 6
↑ Base = six-piece burr
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
↑ # Clips = 6
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
↑ # Clips = 12
↑ Base = cuboctahedron
One clip = one vertex. One handle = one edge.
↑ # Clips = 12
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ # Clips = 30
↑ Base = icosidodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
One clip = one edge.
↑ # Clips = 12
↑ Base = octahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
↑ # Clips = 24
↑ Base = cuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ # Clips = 36
↑ Base = tetrakis hexahedron
↑ Symmetry = pyritohedron’s rotations and reflections = $A_4\times C_2$ of order 24
↑ # Clips = 48
↑ Base = rhombicuboctahedron
↑ Symmetry = cube’s rotations = $S_4$ of order 24
Three clips = one Φ-vertex = one vertex.
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = Φ24-C
Three clips = one Δ-vertex = one vertex.
↑ # Clips = 60
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ # Clips = 180
↑ Vertex config = 5.6.6
↑ Base = truncated icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
Two clips = one X-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = X24-O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = X24-C
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60-I
↑ # Clips = 30
↑ Vertex config = 3.3.3.3.3
↑ Base = icosahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = X60-D
Two clips = one L-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
↑ # Clips = 24
↑ Base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = L24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = L24-C
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = L60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = L60-D
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
Two clips = one I-edge = one edge.
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = I24-O
↑ # Clips = 24
↑ Base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I24-C
↑ # Clips = 30
↑ Vertex config = 5.5.5
↑ Base = dodecahedron
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I60-I
↑ # Clips = 30
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ dual = I60-D
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = I36-kT
↑ # Clips = 48
↑ Base = cuboctahedron
↑ Vertex config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I48-jC
↑ # Clips = 72
↑ Base = truncated cube
↑ Vertex config = 3.8.8
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = triakis octahedron)
↑ # Clips = 72
↑ Base = truncated octahedron
↑ Vertex config = 4.6.6
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = tetrakis hexahedron)
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = deltoidal icositetrahedron)
↑ # Clips = 120
↑ Base = snub cube
↑ Vertex config = 3.3.3.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = pentagonal icositetrahedron)
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I120-jD
↑ # Clips = 180
↑ Base = truncated icosahedron
↑ Vertex config = 5.5.6
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I180-kD
↑ # Clips = 240
↑ Base = rhombicosidodecahedron
↑ Vertex config = 3.4.5.4
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ # Clips = 300
↑ Base = snub dodecahedron
↑ Face config = 3.3.3.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ (Dual = pentagonal hexecontahedron)
↑ # Clips = 36
↑ Face config = 3.6.6
↑ Base = triakis tetrahedron
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = I36-tT
↑ # Clips = 48
↑ Base = rhombic dodecahedron
↑ Face config = 3.4.3.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I48-aC
↑ # Clips = 72
↑ Base = tetrakis hexahedron
↑ Face config = 4.6.6
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ Dual = I72-tO
↑ # Clips = 120
↑ Base = rhombic triacontahedron
↑ Face config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I120-aD
↑ # Clips = 120
↑ Base = pentakis dodecahedron
↑ Face config = 5.6.6
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I180-tI
↑ # Clips = 240
↑ Base = chamfered dodecahedron
↑ Each dodecahedron vertex = 4 new vertices
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = I240-uI
↑ # 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
↑ # Clips = 12
↑ Base = tetrahedron
↑ Vertex config = 3.3.3
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ Dual = itself
↑ # Clips = 24
↑ base = cube
↑ Vertex config = 4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = W24-O
↑ # Clips = 24
↑ base = octahedron
↑ Vertex config = 3.3.3.3
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ dual = W24-C
↑ # Clips = 60
↑ Base = dodecahedron
↑ Vertex config = 5.5.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = W60-I
↑ # Clips = 60
↑ Base = icosahedron
↑ Vertex config = 3.3.3.3.3
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
↑ Dual = W60-D
↑ # Clips = 36
↑ Base = truncated tetrahedron
↑ Vertex config = 3.6.6
↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12
↑ # Clips = 120
↑ Base = icosidodecahedron
↑ Vertex config = 3.5.3.5
↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60
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!)
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.