A classification theorem for Zindler carousels (Q1868371)

The main object of the paper is the Zindler carousels, i.e. systems of \(n\) smooth curves \(\{ \beta_1(t)\dots \beta_n(t)\}\) in \(\mathbb{R}^2\) satisfying the following properties: (1) \(| \beta_{i+1}(t)-\beta_{i}(t)| = \text{const} \neq 0\). (2) The curve \(m_i(t)=(\beta_i(t)+\beta_{i+1}(t))/2\) has tangent vector \(m'_i(t)\) parallel to \(\beta_{i+1}(t)-\beta_i(t)\). (3) The curves \(\beta_i(t)\) are reparametrizations of the same closed curve. The paper gives the complete classification of Zindler carousels with five chairs (i.e. \(n=5\)).