OctoSurface to Gyroid Lattice Transition Cylinder

gyroid OctoSurface.stl

Stepped Octasphericon (Single and Dual Color Versions)

sidea-solid.stl

Ruler

Part Studio 1 - Ruler.stl

SKELETAL P SURFACE CELL

Cube1020SkeletalPSurface.3mf

Clifford Sculptures (Core)

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!


FRD Lattice Cell

1.3mf

Tautochrone Track

ttrack.STL

High Rolling Rigged Dice

Rigged+for+6.stl

4x4 Tsugite Cube Puzzle

4x4_White.stl

קוביות האלפבית העברי
Isohedral

Hebrew Alphabet d22 Polyhedral Die

קוביות האלפבית העברי
Isohedral fair die with every Hebrew letter on its faces.

Math

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OctoSurface to Gyroid Lattice Transition Cylinder

Stepped Octasphericon (Single and Dual Color Versions)

Ruler

SKELETAL P SURFACE CELL

Clifford Sculptures (Core)

FRD Lattice Cell

Tautochrone Track

High Rolling Rigged Dice

4x4 Tsugite Cube Puzzle

Hebrew Alphabet d22 Polyhedral Die

Magnetic Numbers

The MATHEMATIK

Fractal Coasters - 7 Unique Designs

Geometric Vase

Icosahedron Earth // Folding Polyhedra

Cube Holder: Kinetic Desk Sculpture

Stretched Cylindrical Gyroid Structure

UFO of BABYLON Puzzle

Sin/Cos Stencil

Aizawa Strange Attractor Sculpture