The Hopf fibration of the great dodecahedron maps its vertices to according great circles, its edges into twisted (i.e. non-flat but smoothly curved) faces (then looking like a Möbius strip), and the faces get mapped into twisters, which are solid rings bounded by those twisted faces and having thereby throughout the polygonal cross-section of the pre-image, i.e. are pentagonal here. Further each twister then gets dissected into n identical chiral antiprisms. This isochoric construction moreover happens to come out to be isogonal as well, so in total provides a noble polychoron.

This polychoron will have 2 types of edges, one describes the right-up lacing edges of the antiprisms (y), while all its remaining edges belong to the other type (x), simply because the neighbouring twister attaches its cross-secting base polygons next to the left-up lacings of the former. That is, the whole polychoron happens to be chiral in general.

In fact, right this connectedness of the mutually swirling individual twisters does further restrict that n after all. This thus brings back into play the former vertex figure of the starting polyhedron – in addition to the so far only considered faces thereof (the cross-sections of the twisters, i.e. the bases of the antiprisms). Because there also is a full inversion symmetry of the outcome of that fibration, we thus finally have to consideder n = LCM(p, q, 2) for a starting polyhedron {p, q}, i.e. n = LCM(5, 5/2, 2) = 10 in here.

For that specific value this swirlchoron then becomes sisp. Then the edge length ratio can be evaluated as y : x = 1, i.e. sisp will be uniform and esp. the paps happen to become achiral.

Incidence matrix

12n |   2  10 |  15   5 |  10
----+---------+---------+----
  2 | 12n   * |   5   0 |   5  y, edge figure: {5/2}
  2 |   * 60n |   2   1 |   3  x
----+---------+---------+----
  3 |   1   2 | 60n   * |   2
  5 |   0   5 |   * 12n |   2  {5}
----+---------+---------+----
 10 |   5  15 |  10   2 | 12n  chiral pap variant