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!


Vase

model416.stl

Plain Goose update pack

left foot.stl

Heart Swing String Art 

Heart couple.stl

Zephyr_Nimbus_Radial_Art.stl

Mini Dragon Skeleton

mini dragon skeleton.stl

Boston Terrier Dog Yoga Pose 3

Boston Yoga 3 body.stl

French Bulldog Dog Yoga Pose 1

Pose 1 - BodyV2.stl

Cactus Middlefinger - Fucktus

Fucktus With Flowers One Middle Finger (Color File).stl

Geometric Lion wall art - A

geometric-lion1_full.stl

Elegant Skeleton Bust Holding Roses

Skull_Gentleman.3mf

Pumpkin Booknook 

pumpkin booknook  base.stl

Hanging heart Decorations, 2 styles.

hangiong heart small rose.stl

Floral Puppy 

Floral Puppy.stl

Mini Ghosts

mini ghost.stl

English Bulldog Dog Yoga Pose 1

English Bulldog 1 body with rolls.stl

Geometric Star/Sun wall design

D.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.


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Clifford Sculptures (Carousel)

Vase

Plain Goose update pack

Heart Swing String Art

Zephyr_Nimbus_Radial_Art.stl

Mini Dragon Skeleton

Boston Terrier Dog Yoga Pose 3

French Bulldog Dog Yoga Pose 1

Cactus Middlefinger - Fucktus

Geometric Lion wall art - A

Elegant Skeleton Bust Holding Roses

Pumpkin Booknook

Hanging heart Decorations, 2 styles.

Floral Puppy

Mini Ghosts

English Bulldog Dog Yoga Pose 1

Geometric Star/Sun wall design

120-Cell Study

Complex Barrel Cam Writing Machine

Frog in a Duck Float Figurine — Vinyl-Style Collectible