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Add almost-rings of polyhedra

Vectornaut 2025-07-08 20:56:29 +00:00
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Test-problems.md

@ -122,16 +122,38 @@ Rhombic ring of icosahedra
- **Author:** RobertLovesPi
- **Published:** [“A Rhombic Ring of Icosahedra, Leading to a Rhombic Dodecahedron Made of Icosahedra.”](https://robertlovespi.net/2015/09/15/a-rhombic-ring-of-icosahedra-leading-to-a-rhombic-dodecahedron-made-of-icosahedra/) RobertLovesPi.net (September 15, 2015).
Almost-ring of 48 tetrahedra
- **Author:** Ian Stewart
- **Published:** “Steinhaus’s Problem on Chains of Regular Tetrahedra.”
Quadrahelix and octahelix
- **Author:** Michael Elgersma and Stan Wagon
- **Published:** “The Quadrahelix: A Nearly Perfect Loop of Tetrahedra.” [`arXiv:1610.00280`](https://doi.org/10.48550/arXiv.1610.00280) (November 7, 2016).
Almost-ring of thirteen square anti-prisms
- **Author:** Jim McNeill
- **Published:** [“A ring of anti-prisms”](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/aprism-rings.html). [Polyhedra](https://www.orchidpalms.com/polyhedra/).
#### Statement
Choose a rigid ring of polyhedra. Assemble it by constraining distances between vertices or angles between faces.
Choose a rigid ring or almost-ring of polyhedra. Assemble it by constraining distances between vertices or angles between faces. If it's a ring, verify that it closes and is rigid. If it's an almost-ring, verify that it doesn't close.
#### Notes
Here are some examples of interesting rings:
- A ring of eight dodecahedra
- A [rhombic ring](https://robertlovespi.net/2015/09/15/a-rhombic-ring-of-icosahedra-leading-to-a-rhombic-dodecahedron-made-of-icosahedra/) of eight icosahedra
- [A rhombic ring of eight icosahedra](https://robertlovespi.net/2015/09/15/a-rhombic-ring-of-icosahedra-leading-to-a-rhombic-dodecahedron-made-of-icosahedra/)
Here are some examples of interesting almost-rings
- An almost-ring of 48 tetrahedra (Stewart 2023, Figure 2)
- A quadrahelix almost-ring of tetrahedra (Wagon and Elgersma, 2016)
- An octahelix almost-ring of tetrahedra (Wagon and Elgersma, 2016)
- [An almost-ring of thirteen square anti-prisms](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/aprism-rings.html)
## Exploring configuration spaces