Asdymmetric Caltrop

This CAD model was designed by Oskar van Deventer, copyright (c), 26 September 2025.

Asymmetric Caltrop is caltrop with 31 spikes. Regular caltrops have four spikes in a tetrahedral configuration. This object always falls such that one spike is straight up, ready to puncture tires. One can easily design a six-spike caltrop based on the geometry of a pentagonal pyramid. It has the same property that there will always be one spike straight up, when it rests on a flat surface. Surprisingly, Asymmetric Caltrop also has this same property. There will always be a spike straight up. Conversely, one can point each of the spikes straight up, and the object can rest on a flat surface. 

The geometry of the object is based on an isohedral variation of the pentagonal icositetrahedron (https://en.wikipedia.org/wiki/Pentagonal_icositetrahedron). That object has 24 faces and 38 vertices, where each faces has an exactly-opposing verex, but not vice versa. By adding 7 faces and removing 7 vertices, the resulting object has 31 faces and 31 vertices, each face exactly opposing a vertex, AND vice versa. The object has several local 3-fold and 4-fold rotation symmetries, but no over-all symmetry.

An open question is whether there exist other asymmetric N-spike caltrop, with N smaller than 31.

Here are some links about this design.
https://www.youtube.com/watch?v=ECalH0X7zHY

Feel free to 3D-print an extra sample to give to a friend, as long as you mention the designer and don't charge money.

If you are planning to sell some samples, then please contact me for a license agreement. The royalty fee is 10% of your selling price.

Please do not upload the design to a commercial service, or redistribute the design in any way other than linking to the YouTube video: https://www.youtube.com/watch?v=ECalH0X7zHY

Enjoy!

Oskar
11 October 2025

Contact: 
https://oskarvandeventer.nl/index_contact.php?subject=Print%20It%20Yourself