This paper describes a method to efficiently define and 3D print unique kaleidoscopic hypercomplex fractals. The proposed method allows the user to easily edit fractals in three ways: changing the power the fractal is raised to, changing the number of sides of the kaleidoscope, and the angle and position of the fractal, which creates different shapes due to the kaleidoscope. In the example of the Mandelbulb and the inverted Mandelbulb fractals, where the shape of fractals is manipulated through the kaleidoscopic effect, we create 3D fractal sculptures that can be realised as physical objects by using 3D printing. The flexible parametrisation of the fractal definition implemented as the Houdini tool allows the definition of many unique shapes of kaleidoscopic hypercomplex fractals that can be digitally fabricated with a little pre-processing. The paper results can be used for creating fractal-based sculptures as a part of 3D fractal art.