Gyroid Sculpture #2

Gyroid Sculpture 2.stl

Gyroid Sculpture #1

Gyroid Sculpture 1.stl

Magnetic Gyroid Construction Kit

Do Not Print.stl

120-Cell Sculpture: Two Solid Rings 

120 Cell Sculpture Two Solid Rings.stl

120-Cell Sculpture: Two Intertwining Rings 

120-cell Two Intertwined Edge Rings.stl

120-Cell Polychora Planter

This Polychora Planter is derived from the four-dimensional 120-cell 4-polytope, or polychoron.

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells. 

4-polytopes cannot be seen in three-dimensional space due to their extra dimension, but there are several techniques that can be used to “project” 4-polytopes into three-dimensional space. This design uses the cell-centered stereographic projection method, chosen for the interesting aesthetic appearance.

While these three-dimensional shapes have curved faces and edges of various lengths, it is interesting to imagine that in four-dimensional space, the faces are flat, and the edges are straight and identical in length.

In this design, select cells have then been removed to allow better visualization of the inner cells, and the outer cells have been hollowed for uses as planters of containers of some kind.


120-Cell Sculpture: Six Intertwining Rings

This sculpture highlights the edges of sets of intertwining rings related to Hopf fibrations within the four-dimensional 120-cell 4-polytope.

Because the shapes exist in four-dimensional space, special mathematical techniques are required to visualize them. These sculptures are made using the cell-centered stereographic projection method to create three-dimensional “shadows” of the original four-dimensional shapes. 

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells and can be partitioned into twelve 10-cell great circle rings related to the Hopf fibrations.  The lines in this sculpture outline the edges of six of the intertwining rings, for a total of 60 cells.


120-Cell Edge Sculpture

120-Cell Rings

120-cell Linked Rings.stl

120-Cell Study

The 120-cell is a four-dimensional shape composed of 120 dodecahedral cells. It is one of the six regular convex 4-polytopes and has some of the most beautiful patterns and symmetries.

4-polytopes cannot be seen in three-dimensional space due to their extra dimension, but there are several techniques that can be used to “project” 4-polytopes into three-dimensional space. This study uses the cell-centered stereographic projection method, chosen for the interesting aesthetic appearance.

While these three-dimensional shapes have curved faces and edges of various lengths, it is interesting to imagine that in four-dimensional space, the faces are flat, and the edges are straight and identical in length.

In this 120-cell study, select cells have been removed to allow maximal viewing of the various cells, including the center cell. The outer “shell” of cells has been removed to allow better visualization of the inner cells, and because their relative size is so large compared to the inner cells.


Fischer Koch C(Y) Egg

Fischer-Koch C(Y) Egg.stl

Malfunctioning Plate and Saucer 

Plate.stl

Fischer-Koch C(Y) Lampshade

Lampshade Fischer-Koch C(Y) 200mm.stl

Easter Eggshell 9

Eggshell 9 Hexagonal.stl

Pi Meditation Beads

Pi Beads 36 Ring Spheres.stl

Pi Plate

This Pi Plate make embossed with over 360 digits of pi. It’ll make a great addition to your “Pi Day” party!

See here for video: https://youtu.be/wBeyTwRGXNg 

See here for accompanying “Pi Pan”: https://thangs.com/mythangs/file/54524 

Pi Day is an annual celebration of the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in the month/day format) since 3, 1, and 4 are the first three significant digits of π.

Pi Day is often celebrated with pie due to a pun based on the words "pi" and "pie" and the coincidental circular shape of many pies.

If you want to rock this year’s Pi Party, this is the kitchenware you’re going to need.

For best resolution of text, print with a 0.4mm nozzle.


Four Minimal Surface Fluted Vases

Minimal Surface Fluted Vase - Gyroid.stl

Decorative Minimal Surface Lightbulbs

Light Bulb Schwarz P.stl

Four Minimal Surface Coasters

This model is for display only! Do not print this model!

All Coasters.stl

Ten Minimal Surface Ornaments and Spheres

This file is for display purposes only! Do not print! 

Ten Minimal Surface Spheres.stl

Clifford Sculptures (Climber)

This sculpture is one in a series of three derived from the Clifford parallel geodesics of the cell-centered stereographic projection of the four-dimensional 600-cell. Visit my page for links to others in this series. See here for video: https://youtu.be/MTMeT03aBJ0 

The 600-cell is a stunningly beautiful regular 4-polytope, but its beauty is nearly impossible to appreciate because, well, we can only perceive three dimensions!

One way to deconstruct and appreciate the 600-cell is to understand it in terms of geodesic great circles. The 600-cell is made up of 72 great decagons. The 72 great decagons can be divided into 6 sets of 12 non-intersecting Clifford parallel geodesics, such that only one decagonal great circle in each set passes through each vertex, and the 12 decagons in each set reach all 120 vertices.

When exploring or printing these sculptures, I encourage you to orient to the geometry by first locating the complete decagons. Every line portion of is course part of a larger great decagon that has been removed to reduce complexity and highlight specific aspects of the geometry.

These are advanced sculptures to print and require meticulous planning and support structures. The models pictured were printed with an FDM printer, 0.4mm nozzle at 0.1mm layer height, although these designs are probably better suited to SLA or SLS printing technology.

This project was inspired by the book "Visualizing Mathematics with 3D Printing" by Henry Segerman.

Learn more about Clifford parallel geodesics and 600-cell geometry here: https://en.wikipedia.org/wiki/600-cell 

Clifford Carousel

Named because of its circular symmetries, this sculpture is the easiest to print. It is made up of nine of the smallest Clifford parallel geodesics connected with “struts” to form three interconnected 30-tetrahedron Boerdijk–Coxeter helix rings. 

Clifford Core

Named because of its similarity to an apple core, this sculpture does not contain any full geodesic great circles, but instead shows the interrelation between portions of eleven geodesic great circles, one through the middle and ten twisting around. The sculpture can also be seen as portions of five twisted Boerdijk–Coxeter helix rings containing 21 of the full 30 tetrahedrons.

Clifford Climber

Named for is similarity to playground climbing structures, this sculpture contains nine of the largest Clifford parallel geodesics which, like the “Clifford Carousel,” are connected with “struts” to form three interconnected 30-tetrahedron Boerdijk–Coxeter helix rings. This sculpture is the most difficult to understand and by far the trickiest to print!


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Gyroid Sculpture #2

Gyroid Sculpture #1

Magnetic Gyroid Construction Kit

120-Cell Sculpture: Two Solid Rings

120-Cell Sculpture: Two Intertwining Rings

120-Cell Polychora Planter

120-Cell Sculpture: Six Intertwining Rings

120-Cell Rings

120-Cell Study

View 25 new models

Malfunctioning Plate and Saucer

Fischer-Koch C(Y) Lampshade

Easter Eggshell 9

Pi Meditation Beads

Pi Plate

Four Minimal Surface Fluted Vases

Decorative Minimal Surface Lightbulbs

Four Minimal Surface Coasters

Ten Minimal Surface Ornaments and Spheres

Clifford Sculptures (Climber)