Magnetic Gyroid Construction Kit

Do Not Print.stl

Schwarz P Tealight Holder

This design is part of a set of Tealight Holders derived from mathematical surfaces and lattices. 

The Tealights will print without supports, but you may want to ensure your machine is well calibrated for bridging and that you are getting good layer adhesion.

See here for video: https://youtu.be/ApTyuPGk7EQ


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

Penrose P3 Pods

Display Do Not Print.stl

Clifford Sculptures (Carousel)

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 perceive 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!


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.


Penta Tubes

PentaTube Display Only Do not print.stl

120-Cell Rings

120-cell Linked Rings.stl

Industrial Cinquefoil Stairs

Industrial Cinquefoil Stairs.stl

Ultimate Pasta

This is the ultimate piece of pasta. If you have a Pasta Printer you could print it for World Pasta Day on October 25 or US National Pasta Day on October 17.

See here for video: https://youtu.be/4qpxfTHBdzM 

This playful sculpture is derived from a matrix of Kelvin polyhedra, a fourteen-sided polyhedron with 6 squares and 8 hexagons. A triagonal piece of pasta is stuck on to each hexagonal face. This structure is also known as 8-srs. Yum.


Chrysanthemums

Chrysanthemum 3.stl

Icosahedron

Icosahedron.stl

カタカナアルファベットサイコロ
Isohedral fair

Katakana Japanese Alphabet d48 Polyhedral Die

カタカナアルファベットサイコロ
Isohedral fair die with every Katakana symbol on its faces. Note that usually only 46 Katakana symbols are used. In this model two practically obsolete symbols ヰ and ヱ are used in order to obtain an isoheral 48-hedron

Katakana Japanese Alphabet 48-hedron

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!


Industrial Torus Stairs

Industrial Torus Stairs - With Supports.stl

March Magnets - Day 7 #marchmagnets | Pie with pi symbol and crust with 3.14 (and more digits)

March Magnets_Day 7_Karen Chau Designs.3mf

Tetrahedron

Tetrahedron.stl

Clifford Sculptures (Core)

Cube

Cube.stl

Ⲍⲁⲣⲓⲁ ϯⲙⲉⲧⲣⲉⲙⲛ̀ⲭⲏⲙⲓ ⲁⲗⲫⲁⲃⲏⲧⲟⲩ


Coptic Alphabet d32 Polyhedral Die

Ⲍⲁⲣⲓⲁ ϯⲙⲉⲧⲣⲉⲙⲛ̀ⲭⲏⲙⲓ ⲁⲗⲫⲁⲃⲏⲧⲟⲩ
Unique non-Isohedral die with every Coptic (Egyptian) letter on its faces.
Note that this die is based on order-6 truncated hexakis hexahedron, which has two types of faces, however the die is still fair because the areas of the faces were balanced in such a way that they have the same probability of being landed on.


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Magnetic Gyroid Construction Kit

Schwarz P Tealight Holder

120-Cell Sculpture: Six Intertwining Rings

Penrose P3 Pods

Clifford Sculptures (Carousel)

120-Cell Study

Penta Tubes

120-Cell Rings

Industrial Cinquefoil Stairs

Ultimate Pasta

Chrysanthemums

Icosahedron

Katakana Japanese Alphabet d48 Polyhedral Die

Clifford Sculptures (Climber)

Industrial Torus Stairs

March Magnets - Day 7 #marchmagnets | Pie with pi symbol and crust with 3.14 (and more digits)

Tetrahedron

Clifford Sculptures (Core)

Cube

Coptic Alphabet d32 Polyhedral Die