From 6cc180e41668647bef6c2762c6fdcca063b48852 Mon Sep 17 00:00:00 2001 From: Vectornaut Date: Tue, 27 May 2025 22:32:02 +0000 Subject: [PATCH] Mention kaleidocycle non-self-intersection condition --- Test-problems.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/Test-problems.md b/Test-problems.md index 329dfd5..3a6fbc2 100644 --- a/Test-problems.md +++ b/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.