76-Spike Caltrop

This CAD model was designed by Oskar van Deventer, copyright (c), 29 November 2025.

76-Spike Caltrop is caltrop with 76 spikes. It was suggested by Ben Streeter after seeing my Asymmetric Caltrop, which has 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 of feet. 76-Spike 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. One can easily design caltrops that have some symmetry. The challenge was to have one that has no overall symmetry. 

The geometry of the object is based on an isohedral variation of the pentagonal hexecontahedron (https://en.wikipedia.org/wiki/Pentagonal_hexecontahedron). That object has 60 faces and 92 vertices, where each faces has an exactly-opposing vertex, but not vice versa. By adding 16 faces and removing 16 vertices, the resulting object has 76 faces and 76 vertices, each face exactly opposing a vertex, AND vice versa. The object has several local 3-fold and 5-fold rotation symmetries, but no over-all symmetry. This particular arrangement was found by Ben Streeter through a semi-automated search. The goal was to pure 16 of the 92 spike, such that the resulting caltrop was as balanced as possible.

An open question is whether there exist asymmetric caltrops, other than the 31- and 76-spike ones found so far?

Here are some links about this design.
https://www.youtube.com/watch?v=xx
https://twistypuzzles.com/forum/viewtopic.php?p=437282#p437282

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=xx

Enjoy!

Oskar
29 November 2025

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