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Mention kaleidocycle non-self-intersection condition

Vectornaut 2025-05-27 22:32:02 +00:00
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Test-problems.md

@ -85,6 +85,10 @@ According to Dan Piker, the configuration space of right-angled equilateral hept
A kaleidocycle has seven degrees of freedom: six from the Euclidean motions and one from twisting.
#### Notes
In the notes [“Kaleidocycles with 6 Disphenoids,”](https://www.kociemba.org/themen/kaleidocycles/intro.html) Herbert Kociemba describes the edge lengths of all kaleidocycles that can be realized and rotated through a full twist without self-intersecting.
#### Solution
The unit test [`tangent_test_kaleidocycle`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L814-L881) uses a kaleidocycle and initial configuration for which the infinitesimal twist motion can be written algebraically and verified by hand. To verify it, take the derivatives of the distances between the connected vertices of the kaleidocycle and confirm that they vanish at the configuration space tangent vector that we claim generates the twist motion.