3D-Printed Sculpture

This page contains a selection of 3D-printed mathematical sculpture designed by Robert Fathauer. Some of the designs are available as free stl downloads. The copyrights for these designs belong to Robert, but you're welcome to download the files for your own use. Please credit Robert if you show photos on social media or elsewhere. For commercial uses, please contact rob at tessellations.com.

   

Walkable (5,3) Torus Knot
$44.95
This ten-crossing knot is mathematically described as the (5,3) torus knot. This design is an imagined structure that could be walked by people using stairs. Approximately 3-1/2" across.

   

Walkable Borromean Rings
$34.95
The Borromean rings are three interlocked rings with the property that removal of any one would leave the other two uncoupled. They have been used as symbols in a variety of settings dating back at least to the 7th century. This design imagines a Borromean-ring structure that could be walked by people using stairs. Approximately 4" across (2-5/8" for a single ring).

If you'd like to print one yourself, click here to download the stl file. Permission is only granted to print a copy for yourself, not to distribute the file elsewhere.

   

Walkable Five-Crossing Knot
$44.95
There are two mathematically distinct knots with five crossing. This one is designated 5(1). This design is an imagined structure that could be walked by people using stairs. Approximately 4" across.

If you'd like to print one yourself, click here to download the stl file. Permission is only granted to print a copy for yourself, not to distribute the file elsewhere.

   

Hilbert Tower - Large
$59.95
This model was created by thickening the line of a particular iteration of the Hilbert space-filling curve to allow it to be divided into squares. The squares were then imagined as steps in a sort of tower, creating an enigmatic path over an architectural object. Approximately 4" tall.

If you'd like to print one yourself, click here to download the stl file. Permission is only granted to print a copy for yourself, not to distribute the file elsewhere.

   

Hilbert Tower - Small
$34.95
This model was created by thickening the line of a particular iteration of the Hilbert space-filling curve to allow it to be divided into squares. The squares were then imagined as steps in a sort of tower, creating an enigmatic path over an architectural object. Approximately 3" tall. Note the photo shows the 4" tall version.

If you'd like to print one yourself, click here to download the stl file. Permission is only granted to print a copy for yourself, not to distribute the file elsewhere.

   

Fractal Crystal
$44.95
This fractal object is constructed by starting with a first generation cube and placing a half-scale cube on the center of each face. The second-generation cubes have the same orientation as the first-generation cube. Third-generation cubes again scaled by half are placed on each unoccupied face of a second-generation cube. This process is continued ad infinitum to form a "fractal crystal". The growth of the crystal occurs more rapidly along normals to the faces of the starting cube, leading to an overall envelope (convex hull) that is an octahedron, the Archimedean dual of the cube. The sculpture includes the first 6 generations of cubes. The classical fractal known as a Sierpinski triangle occurs over and over throughout the sculpture. Approximately 2.9" along a diagonal.

   

Eight Cubes Fractal Sponge
$67.50
This fractal structure was obtained by starting with eight cubes stacked to form a larger cube. One of the eight was removed, and the resulting polyhedron was scaled down and substituted for each of the other seven. Iterating these steps leads to a fractal exhibiting Sierpinski-triangle-like facets. This model contains five generations altogether. Approximately 2" on a side.

   

Dragon Cubes
$49.95
This fractal arrangement of cubes defines a generation of the twin dragon curve at each iteration. I.e., the curve deveops spatially. This arrangement was discovered by noting that a Phythagorean tree can be folded into a dragon curve, and that four of these could be put together to form an arrangement of cubes. There are nine generations of cubes in this model, with a scaling factor of root 2 between successive generations. Height approximately 3".

   

Hilbert Block
$29.95
This model was created by extruding a particular iteration of the Hilbert space-filling curve and then taking the intersection of two such extrusions. Approximately 1-1/2" (3-1/2 cm) across.

If you'd like to print one yourself, click here to download the stl file. Permission is only granted to print a copy for yourself, not to distribute the file elsewhere.

   

Cubes Fractal
$48.95
This is a fractal arrangement of cubes, starting with a single cube and then iteratively adding several generations of half-scaled cubes. Approximately 2.8" (7 cm) across.