I call this style of tensegrity an n-m prism. These tensegrities have a tendon structure consisting of a regular n-gon prism. The struts then connect vertices from opposite sides of the prism, with some offset m from directly adjacent vertices. Larger n produces a more rounded top and bottom. Smaller m results in the internal hole being larger (up to a point). By symmetry an n-m prism is the same as an n-(n-m) prism after reflection. A 2n-n prism would have all of its struts intersecting in a single point, because each strut would connect two points on opposite sides of the prism.
3-1 (3-2) Prism
4-1 (4-3) Prism
The 10-1 prism has a large internal hole when viewed top-down.
The 10-3 prism has a smaller internal hole when viewed top-down.
I call this style of tensegrity an n-m fan. The n denotes the number of ‘blades’ and the m denotes the number of struts in each blade. This pattern is based on a generalization of a tensegrity by Marcelo Pars called Three Fans. It is also related to his Eternal Wave. I would call his Three Fans a 3-17 fan because it has three blades and each blade is comprised of seventeen struts.
A tensegrity based on the tetrahedron is probably the most popularly realized tensegrity. I have explored several variants and different construction techniques on this benchmark tensegrity.
Truncated Tetrahedron (1)
Truncated Tetrahedron (2)
Icosahedron and Dodecahedron
Since tensegrities derived from polyhedra can usually be realized in terms of either the original polyhedron or its dual, I list this under both the icosahedron as well as the dodecahedron.