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Y4 Pendant 3d printed

Not a Photo

14k Rose Gold Plated
Y4 Pendant 3d printed
Y4 Pendant 3d printed

Not a Photo

Y4 Pendant

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  • 3D printed in 14k Rose Gold Plated: Polished brass plated with 14k Rose Gold
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  • This product is intended for mature audiences.
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Product Description

A fourdimensional caltrop illustration as a pendant. - The strangest thing ever.

We live in a threedimensional Euklidian world, it seems. We cannot really imagine fourdimensional objects. (This is true for you and me and other "normal" people.)

The concept of a caltrop has been translated from three dimensions into four ones - and back to three dimensions to get a 3D printable object.

The well oriented 4D caltrop computed by a brute force search is given by 5 vectors below. In OpenSCAD syntax, they read as

  [ a, b, b, b ],
  [ b, a, b, b ],
  [ b, b, a, b ],
  [ b, b, b, a ],
  [ c, c, c, c ]

with a = 1/8 * (3 * sqrt(5) - 1),  b = -1/8 * (sqrt(5) + 1), and c = 1/2.

Remarks: The Euklidian norm of each (line) vector is 1. The sum of all vectors is 0. The scalar product of any two different vectors is -1/4. The goal was to minimize the difference of the maximum and the minimum of the 20 absolute coordinate values by appropriately rotating the object in 4D space.
Please also refer to the article in German math journal Wurzel 01/2017. -  http://www.wurzel.org

There are three other similar steel models - parts of a puzzle to play with. Enjoy!
For dimension 5 and 6 two more pendants are available: Hexadenton and Heptadenton (Siebensporn).
What's in the Box
Y4 Pendant
14k Rose Gold Plated
2.3 cm
2.4 cm
2.7 cm

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