Acronym setut
Name small tristetracosioctacontachoron
Circumradius 1
Vertex figure
 ©
General of army ex
Colonel of regiment sishi
External
links
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As abstract polytope setut is isomorphic to getut, thereby interchanging the orientation of its thahs.

As can be seen from its vertex figure setut-verf, also displayed above, there are a total of 4+12 tets incident to each vertex (as seen from the according red triangles there). The 4 of those triangles have all 3 sides of type "red-blue", while the others have only 2 sides each of that type and a further side each of type "red-yellow". None the same all those tets would belong into the same equivalence class in here, in fact those are just trigonal pyramids wrt. outer symmetry instead, one face being of type "red-yellow", all others are of type "red-blue". They simply are being used within different orientations within the vertex figure, therefore looking different there.

Furthermore one observes from the vertex figure as well, that this exceptional side of the (red) tets adjoins to one side of the (yellow) trips. From the other 12 yellow acute triangles of the vertex figure one observes that those connect to blue faces at the sides of the there missing 4 red triangles (then representing pseudo tets). All the blue bowties in turn are vertex figures of the thahs. Thence the (yellow) trips in here not only connect to the (blue) thahs at all of their squares, but also at that opposite triangle too.


Incidence matrix

120 |  12   8 |  12  12   36   48 |  16  24  24
----+---------+-------------------+------------
  2 | 720   * |   2   0    6    4 |   4   4   4
  2 |   * 480 |   0   3    0    6 |   0   3   6
----+---------+-------------------+------------
  3 |   3   0 | 480   *    *    * |   1   1   0  ry
  3 |   0   3 |   * 480    *    * |   0   1   1  by
  3 |   3   0 |   *   * 1440    * |   1   0   1  rb
  4 |   2   2 |   *   *    * 1440 |   0   1   1  by
----+---------+-------------------+------------
  4 |   6   0 |   1   0    3    0 | 480   *   *  r tet
  6 |   6   3 |   1   1    0    3 |   * 480   *  y trip
  6 |   6   6 |   0   1    3    3 |   *   * 480  b thah

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