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

120-Cell Rings

120-cell Linked Rings.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.


Cthulhu Zenyatta - Overwatch - Fanart

Coral Snowflake Wall Sculpture

This sculpture, entitled Coral Snowflake, is crafted from 30 identical 3D printed forms that are assembled into an interlocking hexagonal grid. From: http://herschelshapiro.com/coral-snowflake/

Assembling a 30 piece sculpture as shown in the picture requires 140pcs of #4 x 1/2" Stainless Steel Flathead Self Tapping Screws.

Torus Vase

Torus Vase.STEP

The Infinity Vase

Infinity Vase.STEP

Darth Vader bust (fan art)

darth_vader_bust [eastman].stl

Malfunctioning Plate and Saucer 

Plate.stl

Cyber Skull Flat Bottom

License: Attribution-NonCommercial-NoDerivs
CC BY-NC-ND
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This one is going in my Sugar Skull Collection,

Cyber Skull which is part of a bigger project, Thought I would upload this so that all my BUDS could download and show me the awesome prints. 

I hope you all enjoy this model. 

 ORIGINAL SCULPT * 
stay posted for another project incorporating this model.

Hope you all enjoy

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If you print some of my models please tag me on social media.

www.Twitter.com/carmelo_nazario
www.instagram.com/thecreatorx3d

If you want to help a brother out please consider signing up to my patreon.

www.patreon.com/thecreatorx3d


Duck Feeding Up

License: Attribution-NonCommercial-NoDerivs
CC BY-NC-ND
_____________________________________________

Part of the feeding duck series.
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If you print some of my models please tag me on social media.

www.Twitter.com/carmelo_nazario
www.instagram.com/thecreatorx3d

If you want to help a brother out please consider signing up to my patreon.

www.patreon.com/thecreatorx3d


Duck Feeding Up.stl

Buddha head（generated by Revopoint POP 2）

Flowergirl (generated by Revopoint POP 2)

This Flowergirl model was scanned by Jon.Himself with Revopoint POP 2. You also can download this model from his channel:https://skfb.ly/o88qZ

The Rock Pencil Topper

Did you know that the rocks middle name is Douglas?

The rock pencil topper

Loving Clown

The clown is usually seen as someone who acts funny and clumsy to make his audience laugh, making us think he may be somehow "shallow", but he actually has a big heart and can be a true romantic.

Print this cute clown with a beautiful bouquet of flowers as a decoration or as a gift (_e.g. for the incoming Valentine's Day_) for someone special.
⸻⸻⸻⸻⸻⸻⸻⸻

𝗠𝗬 𝟯𝗗 𝗣𝗥𝗜𝗡𝗧𝗜𝗡𝗚 𝗦𝗘𝗧𝗧𝗜𝗡𝗚𝗦 :

🔸 3D Printer: Anycubic Meha SE / Anycubic Photon Mono
🔸 Nozzle: 0.4 mm
🔸 Slicer: Ultimaker Cura 4.12.1 / Lychee Slicer 3.6.2
🔸 Layer height: 0.16 mm (0.8 mm wall thickness; 6 top / 3bottom layers) / 50um (light-off delay 1 / exposure time 1.6s / lifting speed 4mm/s / lowering speed 6mm/s)
🔸 Infill : 10% / 20%
🔸 Some supports needed
🔸 Printing Temperature: 205°C / Build Plate Temperature: 60°C
🔸 Print speed: 45 mm/sec / Outer Wall Speed: 22.5mm
🔸 Filament: Blue Silk PLA by Eryone / Grey Resin by Anycubic
🔸Size: 3,1 x 5,4 x 8,7 cm (X, Y, Z)
⸻⸻⸻⸻⸻⸻⸻⸻

Don't be shy and upload your make! (If you share it on your socials, please be sure to tag @𝙧𝙖𝙣𝙙𝙤𝙢𝙞𝙯𝙮.3𝙙, so that I can see and re-share it / if you have TikTok, you can also use the hashtag #𝙧𝙖𝙣𝙙𝙤𝙢𝙞𝙯𝙮 when sharing your video)

⸻⸻⸻⸻⸻⸻⸻⸻
𝙏𝙝𝙞𝙨 𝙬𝙤𝙧𝙠 𝙞𝙨 𝙡𝙞𝙘𝙚𝙣𝙨𝙚𝙙 𝙪𝙣𝙙𝙚𝙧 𝙩𝙝𝙚 𝘾𝙧𝙚𝙖𝙩𝙞𝙫𝙚 𝘾𝙤𝙢𝙢𝙤𝙣𝙨 𝘼𝙩𝙩𝙧𝙞𝙗𝙪𝙩𝙞𝙤𝙣-𝙉𝙤𝙣𝘾𝙤𝙢𝙢𝙚𝙧𝙘𝙞𝙖𝙡-𝙉𝙤𝘿𝙚𝙧𝙞𝙫𝙖𝙩𝙞𝙫𝙚𝙨 4.0 𝙄𝙣𝙩𝙚𝙧𝙣𝙖𝙩𝙞𝙤𝙣𝙖𝙡 𝙇𝙞𝙘𝙚𝙣𝙨𝙚.
⸻⸻⸻⸻⸻⸻⸻⸻

𝗜𝗡𝗦𝗧𝗔𝗚𝗥𝗔𝗠 : https://www.instagram.com/randomizy.3d/

𝗖𝗵𝗲𝗰𝗸 𝗠𝗼𝗿𝗲 𝗛𝗲𝗿𝗲 : https://linktr.ee/RandomizY

Clown Flower

Hoopoe

Full.stl

Complex Barrel Cam Writing Machine

This model is for display only! Do not print!

Complex Barrel Cam Writing Machine.stl

Lakshmi on Lotus throne & Kirtimukham

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!


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120-Cell Sculpture: Six Intertwining Rings

120-Cell Rings

120-Cell Study

Cthulhu Zenyatta - Overwatch - Fanart

Coral Snowflake Wall Sculpture

Torus Vase

The Infinity Vase

Darth Vader bust (fan art)

Malfunctioning Plate and Saucer

Cyber Skull Flat Bottom

View 24 new models

Buddha head（generated by Revopoint POP 2）

Flowergirl (generated by Revopoint POP 2)

The Rock Pencil Topper

Loving Clown

Hoopoe

Complex Barrel Cam Writing Machine

View 22 new models

Clifford Sculptures (Climber)

Clifford Sculptures (Core)