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!


Dodecahedron

Dodecahedron v2.stl

Clifford Sculptures (Core)

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.


Coptic Alphabet 32-hedron

النرد الأبجدية العربية
Isohedr

Arabic Alphabet d28 Polyhedral Die

Isohedral fair die with every arabic letter on its faces.

Arabic Alphabet 28-hedron

Lissajous Figure Wall Art Coaster

Lissajous 2mm.step

Игральная кость с Русским алфа

Russian Alphabet d30 Polyhedral Die

Игральная кость с Русским алфавитом
Isohedral fair die with every Russian letter on its faces.
Note that in Russian alphabet there are 33 letters but since there does not exist a proven 33-hedral fair die, this model is based on the rhombic triacontahedron (30-faced solid). 6 letters were grouped in pairs to reduce the number of faces - Е & Ё, Ь &Ъ, Ш & Щ.

Russian Alphabet 30-hedron

Low Poly Horse and Unicorn Magnet Puzzle (No supports, no AMS)

horse_primary_color.stl

Low Poly Dog "beagle" Magnet Puzzle (No supports, no AMS)

dog_primary_color.stl

Low Poly Cow Magnet Puzzle (No supports, no AMS)

pieces_white_color.stl

Icosahedron Solid

Icosahedron Solid.stl

Low Poly Deer Magnet Puzzle (No supports, no AMS)

all_pieces_dark_color.stl

Low Poly Elephant Magnet Puzzle (No supports, no AMS)

Pieces_elephant.stl

Low Poly Sheep Magnet Puzzle (No supports, no AMS)

sheep_primary_color.STL

Dodecahedron Solid

Dodecahedron Solid.stl

Low Poly Fox Magnet Puzzle (No supports, no AMS)

pieces_orange_color.stl

Low Poly Panda Magnet Puzzle (No supports, no AMS)

pieces_white.stl

Low Poly Dragon Magnet Puzzle (No supports, no AMS)

dragon_primary_color.stl

Aizawa Strange Attractor Sculpture

Strange Attractor Abstract Sulpture - Aizawa - Unsupported.stl

Low Poly Skull Magnet Puzzle (No supports)

Low_Poly_Skull_Puzzle.stl

math art

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Clifford Sculptures (Climber)

Dodecahedron

Clifford Sculptures (Core)

Coptic Alphabet d32 Polyhedral Die

Arabic Alphabet d28 Polyhedral Die

Lissajous Figure Wall Art Coaster

Russian Alphabet d30 Polyhedral Die

Low Poly Horse and Unicorn Magnet Puzzle (No supports, no AMS)

Low Poly Dog "beagle" Magnet Puzzle (No supports, no AMS)

Low Poly Cow Magnet Puzzle (No supports, no AMS)

Icosahedron Solid

Low Poly Deer Magnet Puzzle (No supports, no AMS)

Low Poly Elephant Magnet Puzzle (No supports, no AMS)

Low Poly Sheep Magnet Puzzle (No supports, no AMS)

Dodecahedron Solid

Low Poly Fox Magnet Puzzle (No supports, no AMS)

Low Poly Panda Magnet Puzzle (No supports, no AMS)

Low Poly Dragon Magnet Puzzle (No supports, no AMS)

Aizawa Strange Attractor Sculpture

Low Poly Skull Magnet Puzzle (No supports)