Acronym | ... |
Name |
cubiswirlic heptacontidichoron, twelvefold dissected cubic polytwister, twelvefold dissected cubiter |
Circumradius | sqrt[(3+sqrt(3))/2] = 1.538189 |
Face vector | 96, 384, 360, 72 |
Confer |
|
External links |
The Hopf fibration of the cube 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 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 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(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[(3-sqrt(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
© 2004-2024 | top of page |