Dicyclic dancing

This application is intended to give visual representations of dicyclic groups up to order 24. The restriction on order is simply due to space on the screen.

The dicyclic group of order 4n has two generators a and b. The relations are \(a^4=e, a^2=b^n\) and \(aba^{-1}b=e.\) You may notice that this means that the 'dicyclic' group of order 4 is just the cyclic group of order 4. For this reason this group is often excluded.

The visualisation shown in this application uses dancing figures. Buttons enable you to see the dance sequence for \(a, b, a^{-1}, b^{-1}\) and \(aba^{-1}b\).

The figures can be shown in up to four colours and you can choose how to colour them. The first option is , by group, using this option should help you to appreciate the \(b\) dance sequence. The dancers are all given numbers (and the moves correspond to permutations in \(S^{4n}). Another colouring colours dancers using these numbers (mod 4). A third colouring colours dancers using these numbers (mod 2). The final choice just shows one colour.