Print-It-Yourself Puzzles

Currently Playing: Asymmetric Caltrop - Can a caltrop have fewer than 31 spikes and still have no overall symmetry?

Print it yourself at https://oskarvandeventer.nl/Print-It-Yourself/. Buy at 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 vertex, 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 an asymmetric N-spike caltrop, with N smaller than 31. Copyright (c) 2025, M. Oskar van Deventer. Frequently Asked Question: http://oskarvandeventer.nl/FAQ.html Buy mass-produced Oskar puzzles at https://www.puzzlemaster.ca/browse/inventors/oskar/ (USA, CA) and https://www.sloyd.fi/brain-teasers/inventors-designers/oskar-van-deventer (EU) Buy exclusive 3D-printed Oskar puzzles at https://i.materialise.com/shop/designer/oskarpuzzle, https://www.chewiescustompuzzles.com/puzzleshop/oskars-puzzles