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!


Industrial Torus Stairs

Industrial Torus Stairs - With Supports.stl

קוביות האלפבית העברי
Isohedral

Hebrew Alphabet d22 Polyhedral Die

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

Hebrew Alphabet 22-hedron

High Rolling Rigged Dice

Rigged+for+6.stl

March Magnets - Day 14 #marchmagnets | Stackable 1/6 pie slice with whipped cream dollop

March Magnets_Day 14b_Karen Chau Designs.stl

Lissajous Rope Knots

13,14,15,P,P,0.stl

Geometric Vase

GeometicVase.stl

Cube Holder: Kinetic Desk Sculpture

TrappedBall.stl

FRD Lattice Cell

1.3mf

Icosahedron Earth // Folding Polyhedra

large-full-land-all.stl

The MATHEMATIK

Number Base - Chamfer.stl

4x4 Tsugite Cube Puzzle

4x4_White.stl

SKELETAL P SURFACE CELL

Cube1020SkeletalPSurface.3mf

Magnetic Numbers

8.stl

UFO of BABYLON Puzzle

UFO.stl

Astrolabicon Pro // Grid

Astrolabicon_Grid.stl

Fractal Coasters - 7 Unique Designs

RingsFractal.stl

Sin/Cos Stencil

SinCos Stencil.step

Mobius 8 Helix

mobius 8.STEP

Mobius Helix CAD Experiment

mobius helix.STL

math

Most Downloaded of All Time

Categories

Downloads

Trending

Popular

Paid

Videos

New Uploads

Downloads

Trending

Popular

Paid

Videos

New Uploads

Downloads

Clifford Sculptures (Core)

Industrial Torus Stairs

Hebrew Alphabet d22 Polyhedral Die

High Rolling Rigged Dice

March Magnets - Day 14 #marchmagnets | Stackable 1/6 pie slice with whipped cream dollop

Lissajous Rope Knots

Geometric Vase

Cube Holder: Kinetic Desk Sculpture

FRD Lattice Cell

Icosahedron Earth // Folding Polyhedra

The MATHEMATIK

4x4 Tsugite Cube Puzzle

SKELETAL P SURFACE CELL

Magnetic Numbers

UFO of BABYLON Puzzle

Astrolabicon Pro // Grid

Fractal Coasters - 7 Unique Designs

Sin/Cos Stencil

Mobius 8 Helix

Mobius Helix CAD Experiment