Amazing Mathematical Based Sculptures

Zachary Abel is student in the MIT Mathematics department, and his Research focuses on the interactions between geometry and theoretical computer science. He is attempting to reveal hidden geometric beauty in office supplies and other modest materials. Everything will be more clearly when you see these images…


A swarm of colorful hair ties twists and dances through a framework of lollipop sticks; the structure is held in a delicate balance by their mutual tug-of-war. The entire structure is quite small—7cm in diameter, or about the size of a tennis ball.

Möbius Clips

Putting yet another twist on binder clips, these 110 colorful clips are linked by the handles to form a Möbius-like strip. Much like a Möbius strip, this strip has a single side and a single edge. But whereas a true Möbius strip has a single half-twist, this figure has five.

Paperclip Snub Dodecahedron

A snub dodecahedron made from 120 paperclips. I designed this in response to George Hart’s paperclip snub dodecahedron challenge, imposing a few additional constraints of my own: the paperclips should support themselves without glue, solder, etc., and the pieces should be recognizable as paperclips, with as little modification as possible. In this design, half of the paperclips have been bent at the middle, and the other half are intact and outline the central triangles.


The Impenetraball protects its hollow interior with a dense, chainmail-like mesh made from 132 binder clips. The weave pattern complements the dimensions of these binder clips, exploiting the fact that a handle just barely fits around the body of a neighboring clip (both lengthwise and widthwise). This also makes for an assembler’s worst nightmare; a good pair of small needle-nose pliers and a great deal of patience are essential.


The handles of six binder clips weave together in a way that holds all clips open. This “explosive” configuration is quite stable despite its high potential energy. I will leave the construction method as an entertaining puzzle. Here’s a hint: you should need to strain your hands no more than when normally opening a binder clip.


Many binder clips are interlocked into an airy ball composed of 20 hexagons and 12 stars. There are 90 clips but only 120 handles: each clip in the middle of a star is missing one handle. If these were put back in, the polyhedral structure would correspond to a “rectified truncated icosahedron,” obtained by replacing each vertex of a “soccer ball” polyhedron with a triangle.


A subset of an infinite, repeating arrangement of interwoven cylinders, made from 144 wooden skewers and held together with glue. The skewers form four identical, intersecting triangular prisms, giving the figure chiral tetrahedral symmetry—or chiral cubic symmetry if the spiked and non-spiked ends are not distinguished. The high density packing and repetitive lattice pattern create mesmerizing networks of passageways through the sculpture.

Black Hole

Thirty lollipop sticks are pulled toward the middle of the Black Hole by rubberbands; the sticks desperately oppose their crushing doom by bracing against each other. From the equilibrium emerges this dodecahedrally-symmetric form. Each stick is supported against the central pull by four other sticks, and in turn it helps brace four more sticks. So in total, each stick touches eight others.


The Polypolypolyhedron is an orderly mess of 60 woven plastic rods. The rods come in six groups of 5 and 10 groups of 3, where the rods in each group bend their way through the busy central interchange and have their ends fastened to each other with rubber bands. All of the 5-fold groups are identical, as are all 3-fold groups: the figure has dodecahedral symmetry.

Poker Faces

Thirty standard playing cards are carefully slit and assembled into a configuration of six intersecting pentagonal prisms. Four of the prisms display royal flushes, the luckiest hands in poker. This sculpture is quite lucky geometrically as well: it is only possible because the aspect ratio of standard poker cards, namely 88mm/63mm≈1.397, is sufficiently close to 5−5√2≈1.382. This number is the unique rectangle size that allows the prisms’ edges to meet at 12 five-way junctures.

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