7 Interesting 3D Printed Math Art Files to 3D Print
Mathematics and art may seem like distant worlds, but 3D printing has brought them together in astonishing ways. From intricate geometrical patterns to elegant representations of complex equations, 3D printed math art showcases the beauty hidden within numbers and formulas. These projects not only serve as eye-catching sculptures but also as educational tools that make abstract mathematical concepts more tangible. Artists, educators, and designers now use 3D printers to transform theoretical ideas into real-world masterpieces. Whether you're a math enthusiast or simply intrigued by visual elegance, these seven amazing projects will open your eyes to the artistic side of mathematics.
1. 6-Dimensional Klein Bottle
This 3D model is a modern reinterpretation of the classic Klein bottle, a topologically significant object. A true Klein bottle is formed by joining opposite edges of a plane—first by twisting one pair to form a Möbius strip, then connecting the remaining pair. However, in three-dimensional space, this process results in self-intersections, making it impossible to construct a real Klein bottle without compromising its topological properties. Even in digital design, it presents challenges for 3D printing due to issues defining what is solid and what is void, especially when orienting surface normals in a triangulated mesh.
To resolve these difficulties and allow successful fabrication, the model introduces a conceptual twist by embedding an additional spatial dimension. This is represented by an array of toroidal forms (toroids) distributed across the surface. These toroids, deformed by local surface tension and interactions with their neighbors, provide a physical thickness that allows slicer software and 3D printers to interpret the geometry correctly. Each toroid acts as a structural unit, making the surface both visually complex and physically printable. These figures are logical counterparts to the Klein bottle—simpler topological objects formed by pairing sides of a plane without twisting.
The design as a whole becomes a poetic fusion of mathematics and sculpture. It transcends pure geometry and enters the realm of decorative art while staying rooted in topological theory. This thoughtful integration of form and function results in a unique object that captivates both scientifically and aesthetically.
For best printing results, use a layer height of 0.2 mm or 0.16 mm. A large raft is essential to prevent the model from detaching due to bending forces, especially at greater heights. Begin printing slowly to ensure strong bed adhesion. When importing the model into Cura or a similar slicer, scale it to at least 800%—ideally resulting in a final print taller than 12 cm
Download link: Cults3d.
2. Infinity Grid Cube – Optical Illusion Cube Series
The Infinity Grid Cube is a captivating 3D-printed creation that offers an impressive visual experience. Featuring a uniform grid of circular holes on each face, the design creates a tunnel-like illusion that draws the eye in from every angle. It’s a fantastic conversation piece, ideal for use as a desk toy, light diffuser, or striking decorative item. Designed for ease of use, it prints without supports and can be easily scaled or customized with different infill patterns to achieve unique effects. This model is a great way for makers to showcase their printer’s precision with a clean and professional finish.
Download link: Makerworld.
3. Mystical Eye Geometric Dream Catcher/Print-N-Place
This 3D-printed dream catcher is a charming and creative design, especially notable for its articulated, print-in-place links. As the designer’s first attempt at such a model, it showcases both artistry and functionality. The print requires no assembly, making it simple and accessible for all skill levels. Allow the piece to cool completely before removing it from the build plate to prevent breakage, especially around the smaller links. Once cooled, the rings can be rotated to fully extend. Using gradient filament enhances the visual effect by aligning the colors in a flowing, uniform direction across the entire design.
Download link: Makerworld.
4. Menger's Sponge (Fractal Cube, 3D Sierpinski's Carpet)
The model is a fractal cube known as a Menger’s Sponge, or alternatively, the 3D version of the Sierpinski carpet. Characterized by having infinite surface area and zero volume, it becomes computationally demanding to generate as its order increases, both in terms of processing time and memory usage. The designer was able to compute up to the 4th order using a PC but only managed to successfully 3D print the 3rd order version using a budget-friendly FDM printer, challenging others to push the boundaries further.
To create the model, OpenSCAD was used with a base cube module (cube.scad). Due to the complexity of calculations, the 3rd order was the highest feasible with this approach. An alternative method involved creating a fractal corridor using cubedig.scad, which was then copied and rotated along the X, Y, and Z axes before performing a Boolean subtraction from the cube. This technique allowed for a 4th-order design, such as the “cubedig4-dig145.stl” (a 145mm cube corridor), which was later scaled to one-third of its size and refined in Blender to produce “cubedig4_48.33.” Despite these efforts, the designer noted that their 3D printer (Da Vinci) couldn’t handle structures beyond the 3rd order due to the fragility and low density of the print.
Download link: Thingiverse.
5. Hilbert Cube
This striking Hilbert Cube by ErnyCrazyPrinter is a math‑inspired sculpture built for 3D printing, blending fractal geometry with technical ambition. Although the creator aimed to generate a true Hilbert cube, limitations in coding resulted in a structure consisting of three separate Hilbert curves rather than a single continuous path. Still, the resulting form is visually compelling and conceptually intriguing.
The design was generated using a custom Ruby script that produces OpenSCAD code for 1 through 3 iterations of a 3D Hilbert curve. It’s a perfect specimen for experimenting with water‑soluble PVA supports—almost impossible to print cleanly without dissolvable material. Supported prints have successfully utilized dual-filament setups, and the model includes pre-designed support files to streamline the setup process.
Despite not being topologically continuous, the model’s intricate lattice makes it aesthetically pleasing and an excellent mental exercise in both form and fabrication. The community feedback highlights its value as a support‑test object, especially for tackling challenging overhangs and internal voids.
Download link: Cults3d.
6. Gyroid
This Gyroid sculpture showcases the mesmerizing geometry of an infinitely connected triply periodic minimal surface, originally discovered by NASA scientist Alan Schoen in 1970. Presented as a perforated cube, the model captures the organic lattice of a gyroid surface, blending mathematical elegance with visual intrigue. It forms part of a family of artful interpretations that explore variations on the gyroid theme, often combined with Voronoi patterns for added complexity.
Structurally, the design offers both aesthetic appeal and practical functionality. Its interwoven surfaces create a light yet solid architecture that doesn’t require support structures, making it ideal for resin or precise FDM prints as long as print resolution is sufficient. The varying porosity and curved pathways reflect the idealized gyroid infill strategy, yielding both beauty and strength within a compact form
Download link: Myminifactory.
7. Fractal Pyramid With Continuous Cross-section
This visually stunning fractal pyramid—often referred to as the Continuous Cross-Section model—is a half-octahedron structure based on the Sierpiński triangle principle. Each horizontal layer is a single connected shape that evolves seamlessly with height, making it an ideal candidate for spiral vase-mode printing or single-wall slicing without infill. The design elegantly avoids overhangs, bridges, and support issues, producing clean results in compatible slicers.
Ricktu created the model to demonstrate a fractal surface where internal voids comply with the rules of Sierpiński subdivisions. Due to its continuous cross-sections, it has proven especially suitable for resin and filament printers using vase mode, provided the printer has sufficient resolution. Users have successfully printed iterations up to level 5 (i.e., five recursive steps), with base sizes ranging around 100 mm, using PET-G at a layer height of 0.20 mm, with one wall, and without brim or raft.
The design has inspired numerous remixes and variations, including stacked versions and lamp bases designed to showcase transparency with embedded LEDs. Community print logs praise its ease of printing under vase mode and a minimalistic construction approach.
Download link: Thingiverse.
8. Polygonal puzzle - Series 1- Hexagon – Puzzle
This geometric design series draws inspiration from two foundational shapes in mathematics: the hexagon and the hexagram (hexagon star). These iconic forms are not only vital in geometry but also symbolize the elegance of mathematical patterns. By incorporating these shapes into visually engaging designs, the series aims to spark creativity and appreciation for the harmony between math and art. With five planned patterns, each can be individually appreciated or combined to form larger, colorful compositions. Designed as an interactive learning tool, the series encourages children to explore math concepts hands-on. As they assemble pieces and experiment with colors, they naturally develop spatial awareness and a deeper understanding of geometric relationships. Beyond education, the experience fosters curiosity and creativity. Regular updates will bring more designs and opportunities for community engagement, promoting shared learning and a collaborative journey into the beauty of mathematical structures in everyday life.
Download Link: Makerworld.
9. Rhombic Sierpiński Fractal - Level 4 | Vase Mode
This intricate model showcases a Level 4 Sierpiński Octahedron fractal structure, constructed using Rhombic Dodecahedra and optimized for seamless vase mode 3D printing. Designed with intentional gaps and an integrated base, it allows for a continuous spiral print without the need for supports or infill. Ideal for FDM printers, the model should be printed with a 0.4mm nozzle or smaller, using a 0.16mm layer height. Scaling down is not recommended unless a smaller nozzle is used, though scaling up is fully supported.
The print should be done in vase mode with the “smooth spiral” option left unchecked and the slice gap closing radius set to 0.00. This ensures the model slices correctly and prints as intended. The included print profile replicates the results seen in the demo photos. Whether you're drawn to its mathematical elegance or the challenge of printing a geometric fractal, this piece offers a rewarding and visually striking print experience.
Download Link: Makerworld.
10. Mathematical - Multiplication tables Calculator
The Mathematicus – Multiplication Tables Calculator is a clever, 3D-printable educational tool designed to help students practice and internalize multiplication tables through tactile interaction. With a sturdy tabletop format, this print-in-place calculator features sliding markers for both rows and columns, making it intuitive to select two numbers and instantly read their product at the intersection. Its mechanical simplicity means no assembly hassles, and the accompanying print profile (0.2 mm layer height, two walls, 10% infill) ensures smooth, reliable production using PLA and a 0.4 mm nozzle
Ideal as a back-to-school gift or a learning aid, the device has garnered high praise (4.9/5 from over 100 ratings) for its engaging design and educational impact. Community members even modified a hinged cover attachment to hide answers—making it a fun quiz tool for children. Whether in classrooms or at home, Mathematicus offers a hands-on, interactive way to reinforce the fundamentals of multiplication and foster confidence in young learners.
Download Link: Makerworld.
SelfCAD: The Best 3D Printing Software
If you would like to create your own 3D models for math art, you can use various tools, and a good example is SelfCAD. It is an ideal tool for creating 3D printed math art, as it combines intuitive design features with powerful modeling capabilities. With its user-friendly interface, students, educators, and artists can easily visualize and construct mathematical concepts with ease. The video below shows the overview of the software.
SelfCAD's freehand drawing and 2D sketching tools allow users to create precise shapes and mathematical curves, which can then be extruded or revolved into complex 3D forms.
Using the software’s built-in image-to-3D feature, users can even convert mathematical diagrams into 3D models. Once a model is complete, SelfCAD’s integrated slicer prepares it for 3D printing by generating G-code. This eliminates the need for third-party slicing software, streamlining the design-to-print process.
Conclusion
3D-printed math art bridges the gap between abstract concepts and visual beauty. These seven inspiring projects demonstrate how creativity and technology can bring life to mathematics. Whether for learning or admiration, they offer a fresh perspective on how art and math can coexist in truly stunning forms.