The Sierpinski relatives form a fascinating class of fractals because they all possess the same fractal dimension but can look very different. The famous Sierpinski gasket is one of these relatives. The convex hull of the gasket has a boundary that is a right isosceles triangle. There is a sub-class of relatives that all have the same convex hull as the gasket, and are referred to as triangle relatives. The triangle relatives can be used to build other beautiful fractals. In particular, one can build fractals with square convex hulls and these can be used to visualize subgroups of the symmetries of the square.