Industrial Cinquefoil Stairs

Industrial Cinquefoil Stairs.stl

Ten Frame Math Box

ten frame box base (repaired).stl

Ultimate Pasta

This is the ultimate piece of pasta. If you have a Pasta Printer you could print it for World Pasta Day on October 25 or US National Pasta Day on October 17.

See here for video: https://youtu.be/4qpxfTHBdzM 

This playful sculpture is derived from a matrix of Kelvin polyhedra, a fourteen-sided polyhedron with 6 squares and 8 hexagons. A triagonal piece of pasta is stuck on to each hexagonal face. This structure is also known as 8-srs. Yum.


Shale and Roots 

ShaleAndRoots.3mf

Polyhedra Connect-it Tiles - Solid

Octagon_Solid.stl

Snap-Together Gyroid Construction Kit

8 Stars and Squares.stl

SSurface to Gyroid Transition Cylinder

gryoid ssurface50x50.stl

Dodecahedron.step

Tautochrone Track

ttrack.STL

Teaching Triangle - Law of Sines Ambiguous Case

Template.step

Pyramids any-sided Parametric

Pyramids_10.step

The Pi Di.stl

Introducing the PI Di.

This model was uploaded at precisely at 3:14 pm Coordinated Universal Time (UTC) or Greenwich Mean Time (GMT) on March 14 (Pi Day).

Roll the di for fun facts about Pi, including the beautiful symbol itself, the number 3.14, and four formulas to help you measure circles, including the formulas for circumference, diameter, radius, and area.  

Download it now.  Don't be afraid to di.



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!


OctoSurface to Gyroid Lattice Transition Cylinder

gyroid OctoSurface.stl

FRD TPMS Lattice Vase 

decimatedFRDVase.3mf

Industrial Torus Stairs

Industrial Torus Stairs - With Supports.stl

March Magnets - Day 7 #marchmagnets | Pie with pi symbol and crust with 3.14 (and more digits)

math

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Industrial Cinquefoil Stairs

Ten Frame Math Box

Ultimate Pasta

Shale and Roots

Polyhedra Connect-it Tiles - Solid

Snap-Together Gyroid Construction Kit

SSurface to Gyroid Transition Cylinder

Dodecahedron.step

Tautochrone Track

Teaching Triangle - Law of Sines Ambiguous Case

Pyramids any-sided Parametric

The Pi Di.stl

Clifford Sculptures (Climber)

OctoSurface to Gyroid Lattice Transition Cylinder

FRD TPMS Lattice Vase

Industrial Torus Stairs

March Magnets - Day 7 #marchmagnets | Pie with pi symbol and crust with 3.14 (and more digits)

March Magnets - Day 6 #marchmagnets | Lattice pie with pi symbols

Ruler

March Magnets - Day 4 #marchmagnets | Pie with pi symbols