Tetrahedrons // Folding Polyhedra

tetrahedronbig-wire.stl

𐡒𐡅𐡁𐡉𐡅𐡕 𐡄𐡀𐡋𐡐𐡁𐡉𐡕 𐡀

Aramaic alphabet d22 Polyhedral Die

𐡒𐡅𐡁𐡉𐡅𐡕 𐡄𐡀𐡋𐡐𐡁𐡉𐡕 𐡀𐡓𐡌𐡉
Isohedral fair die with every Aramaic letter on its faces.

Aramaic alphabet 22-hedron

Golden Rhombohedra 

Display only do not print.stl

Snap Star

Snap Star Display only do not print.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.


Penta Tubes

PentaTube Display Only Do not print.stl

Weaire-Phelan Tetrastix

Weaire-Phelan Tetrastix Display Only Do Not Print.stl

600-Cell Central Rings.stl

This is a three-dimensional shadow of selected cells of the four-dimensional shape called the “600-cell.”

See here for video: https://youtu.be/IhW48X29e0g 

The 600-cell is one of six regular convex four-dimensional shapes. It is composed of 600 tetrahedral cells.

The full 600-cell is so ridiculously complex that it nearly impossible to see or understand in its entirety, so it is helpful to view it in parts.

If you look closely at this selection of cells, you can see how it is composed of nine interlocking rings connected by “struts.”  In the full 600-cell, these small “struts” are in fact part of complete rings. This gives some idea of how large and complex the full shape would be.

This model is designed for resin printing.


120 Cell.stl

This is a three-dimensional shadow of a four-dimensional shape called the “120-cell.”

See here for video: https://youtu.be/oquFgOw6k28 

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells.

Technically, this model only includes 107 of the 120 dodecahedral cells. The outer layer of cells is proportionally much larger and would be difficult to print. In fact, the outmost cell is infinitely large, which would be very difficult to print.

This is a cell-centered stereographic projection, meaning that there is a single small dodecahedral cell at the center. Can you see it?

This model is designed for resin printing.


Snap Ball (Truncated Icosahedron) 

Snap Ball Display.stl

Snap-Together Gyroid Construction Kit

8 Stars and Squares.stl

120-Cell Sculpture: Two Intertwining Rings 

120-cell Two Intertwined Edge Rings.stl

120-Cell Polychora Planter

This Polychora Planter is derived from the four-dimensional 120-cell 4-polytope, or polychoron.

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells. 

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 design 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 design, select cells have then been removed to allow better visualization of the inner cells, and the outer cells have been hollowed for uses as planters of containers of some kind.


Weaire-Phelan Salver

This “Weaire-Phelan Salver” is part of a set of three tableware pieces inspired by the Weaire-Phelan structure, the most mathematically efficient way for equal-volume bubbles to fit together to make foam. See here for video: https://youtu.be/f4YIuS_-hSE

The Weaire-Phelan structure is made up of two pentagonal dodecahedra (12-sided) and six tetrakaidecahedra (14-sided) that form a translation unit with a lattice periodicity which is simple cubic. In crystallography, this structure is also known as the A15 Frank-Kasper phase.

There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html 


Weaire-Phelan Tumbler

This “Weaire-Phelan Tumbler” is part of a set of three tableware pieces inspired by the Weaire-Phelan structure, the most mathematically efficient way for equal-volume bubbles to fit together to make foam. See here for video: https://youtu.be/f4YIuS_-hSE

This piece could be used as a vase or pencil holder.

The Weaire-Phelan structure is made up of two pentagonal dodecahedra (12-sided) and six tetrakaidecahedra (14-sided) that form a translation unit with a lattice periodicity which is simple cubic. In crystallography, this structure is also known as the A15 Frank-Kasper phase.

There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html 


Weaire Phelan Tumbler

Weaire-Phelan Highball

This “Weaire-Phelan Highball” is part of a set of three tableware pieces inspired by the Weaire-Phelan structure, the most mathematically efficient way for equal-volume bubbles to fit together to make foam. See here for video: https://youtu.be/f4YIuS_-hSE

This piece could be used as a vase or pencil holder.

The Weaire-Phelan structure is made up of two pentagonal dodecahedra (12-sided) and six tetrakaidecahedra (14-sided) that form a translation unit with a lattice periodicity which is simple cubic. In crystallography, this structure is also known as the A15 Frank-Kasper phase.

There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html 


Polyhedra

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View 66 new models

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Golden Rhombohedra

Snap Star

Ultimate Pasta

Penta Tubes

Weaire-Phelan Tetrastix

600-Cell Central Rings.stl

120 Cell.stl

Snap Ball (Truncated Icosahedron)

Snap-Together Gyroid Construction Kit

120-Cell Sculpture: Two Intertwining Rings

120-Cell Polychora Planter

Weaire-Phelan Salver

Weaire-Phelan Tumbler

Weaire-Phelan Highball