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Math PhD @ UIUC

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.

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

2-clip constructions

2face2face

2 binder clips face to face
↑ # Clips = 2

2back2back

2 binder clips back to bacl
↑ # Clips = 2

6-clip constructions

6cycle

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

6wedge

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

6fitin

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

6twist

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

6cross

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

6spike

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

6stand

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

A-series

One clip = one edge.

A12

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

A24

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

A36

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 ↑ (Dual = truncated octahedron)

A48

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

I-series

Two clips = one I-edge = one edge.

I12tetra

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

I24cube

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 = I24octa

I24octa

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 = I24cube

I60dodeca

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 = I60icosa

I60icosa

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 = I60dodeca

I36truncated

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 = I36triakis

I36triakis

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 = I36truncated

I48cubocta

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 = I48rhombic

I48rhombic

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 = I48cubocta

I72truncated

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
↑ (Dual = tetrakis hexahedron)

I96rhombi

96 clips forming 96 I-edges forming snub cube
↑ # Clips = 96
↑ Base = rhombicuboctahedron
↑ Vertex config = 3.4.4.4
↑ Symmetry = cube’s rotations = $S_4$ of order 24
↑ (Dual = deltoidal icositetrahedron)

I120snub

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)

Wiki

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.