A [b]mosaic[/b] is a composition of flat figures that exhibit certain regularity, such as invariance under symmetries or rotations. Follow these steps to construct mosaics using GeoGebra.[br][br][list=1][*]Choose any point A and draw two segments of equal length that meet at A, forming a 60° angle.[/*][*]Construct a non-convex trapezoid using the three points you already have. We will call it[b] T.[/b][br][/*][*]Perform two rotations of [b]T[/b] with respect to point A (it doesn't matter the direction, but both should go in the same direction): one of 60° (which we will call [b]T'[/b]) and another of 120° (which we will call [b]T*[/b]). We will call [b]S[/b] the union of [b]T[/b], [b]T'[/b], and [b]T*[/b] (a new polygon).[br][/*][*]Use the longest side of [b]S[/b] to perform the symmetry of the polygon with respect to that side, called [b]S'[/b]. You will obtain a new polygon [b]R[/b], which is the union of [b]S[/b] and [b]S'[/b].[br][/*][*]Check if [b]R[/b] is invariant under a 60° rotation and find its axes of symmetry (if any).[br][/*][*]Select a diagonal of maximum length (in the direction that is most appropriate for your screen) as a vector and perform [b]successive translations[/b] of the polygon according to that vector (successive means that if the result of translating [b]R[/b] is [b]R'[/b], you need to perform the translation again on [b]R'[/b] to obtain [b]R''[/b], then translate [b]R''[/b] to obtain [b]R'''[/b], and continue in this way until the translations go off the screen).[br][/*][*]Finally, select another diagonal that is different and appropriate, and repeat the procedure. This time, you must translate all the polygons you obtained in step 6).[br][/*][/list][br]To display the resulting mosaic, it is enough to make the names of the elements that are emerging invisible. I recommend doing this from the beginning to avoid complicating the view.[br]