Acronym  ... 
Name 
cubiswirlic heptacontidichoron, twelvefold dissected cubic polytwister, twelvefold dissected cubiter 
Circumradius  sqrt[(3+sqrt(3))/2] = 1.538189 
Confer 

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The Hopf fibration of the cube maps its vertices to according great circles, its edges into twisted (i.e. nonflat 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 crosssection of the preimage, i.e. are squars 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 rightup lacing edges of the antiprisms (y), while all its remaining edges belong to the other type (x), simply because the neighbouring twister attaches its crosssecting base polygons next to the leftup 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 crosssections 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(3, 4, 2) = 12 in here.
For that specific value it results in this swirlchoron. Here the edge length ratio can be evaluated as y : x = sqrt[(3sqrt(3))/2] = 0.796225.
96  2 6  9 3  6 +++ 2  96 *  3 0  3 y 2  * 288  2 1  3 x +++ 3  1 2  288 *  2 4  0 4  * 72  2 +++ 8  4 12  8 2  72 chiral squap variant
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