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.

(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 = 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

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
↑ (Dual = truncated octahedron)

↑ # Clips = 48

↑ Base = rhombicuboctahedron

↑ 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 = I24octa

↑ # Clips = 24

↑ Base = octahedron

↑ Vertex config = 3.3.3.3

↑ Symmetry = cube’s rotations = $S_4$ of order 24

↑ Dual = I24cube

↑ # Clips = 30

↑ Vertex config = 5.5.5

↑ Base = dodecahedron

↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

↑ Dual = I60icosa

↑ # Clips = 30

↑ Base = icosahedron

↑ Vertex config = 3.3.3.3.3

↑ Symmetry = dodecahedron’s rotations = $A_5$ of order 60

↑ dual = I60dodeca

↑ # Clips = 36

↑ Base = truncated tetrahedron

↑ Vertex config = 3.6.6

↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12

↑ Dual = I36triakis

↑ # Clips = 36

↑ Face config = 3.6.6

↑ Base = triakis tetrahedron

↑ Symmetry = tetrahedron’s rotations = $A_4$ of order 12

↑ Dual = I36truncated

↑ # Clips = 48

↑ Base = cuboctahedron

↑ Vertex config = 3.4.3.4

↑ Symmetry = cube’s rotations = $S_4$ of order 24

↑ Dual = I48rhombic

↑ # Clips = 48

↑ Base = rhombic dodecahedron

↑ Face config = 3.4.3.4

↑ Symmetry = cube’s rotations = $S_4$ of order 24

↑ Dual = I48cubocta

↑ # 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)

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.