4.4. Enumeration. The series of uniform helical star deltahedra is infinite because we can start with any number of strips of equilateral triangles. Depending on the number of strips one or more star shapes are possible. And also the possible number of steps in the shifts depends on the number of strips. Starting with five strips we can make two different uniform helical star deltahedra: each has a star shape, combined with a one or a two-step shift (Figures 24-25).
Figure 24: Star 5-2, one step
Figure 25: Star 5-2, two steps
5. Examples

5.1. Infinite Series. The number of uniform helical star deltahedra (UHSD) is infinite. From five to twelve strips however we count 64. Four examples are shown in Figures 26-29. I was surprised by the variety and the beauty of these polyhedra and therefore I have started making real models of these shapes.
Figure 26: UHSD 9-4(1)
Figure 27: UHSD 9-4(2)
Figure 28: UHSD 11-2(2)
Figure 29: UHSD 12-5(3)
5.2. Edges. To get an impression of the internal structure of the polyhedra I made a number of models with only the edges of the equilateral triangles. Figures 30-34 show examples. The model in Figure 34 is constructed with one type of connector (all the vertices are congruent) and pipes of one length only.
Figure 30: Edges of UHSD 5-2(2)
Figure 31: Edges of UHSD 8-3(3)
Figure 32: Edges of UHSD 8-3(1)
Figure 33: Edges of UHSD 7-2(2)
Figure 34: Frame of of UHSD 5-2(2)