Acronym ..., rigfix || quipdohi
Name (degenerate) rigfix atop quipdohi
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
decomposition  

It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D euclidean decomposition of the larger base into smaller bits.

As abstract polytope rigfix || quipdohi is isomorphic to padohi || rofix, thereby interchanging the roles of pentagrams and pentagons, resp. replacing pip by stip, gike by ike, and interchanging the roles of sissid and gad, of peppy and stappy, resp. replacing rigfix by rofix, pippy by stippy, gikagid by ikaid, and quipdohi by padohi.


Incidence matrix according to Dynkin symbol

ox5oo5/2xo3ox&#x   → height = 0
(rigfix || quipdohi)

o.5o.5/2o.3o.    | 720    * |   10   10    0    0 |   10    5   10   20    5    0    0    0 |   2   5    2   10    5   10   10   0   0    0   0 | 1   2   1    5   5 0
.o5.o5/2.o3.o    |   * 1440 |    0    5    5    5 |    0    0   10    5    5    5   10    5 |   0   0    5    5   10    1    5   1   5    5   1 | 0   1   5    5   1 1
-----------------+----------+---------------------+-----------------------------------------+---------------------------------------------------+---------------------
.. ..   x. ..    |   2    0 | 3600    *    *    * |    2    1    0    2    0    0    0    0 |   1   2    0    1    0    2    2   0   0    0   0 | 1   1   0    1   2 0
oo5oo5/2oo3oo&#x |   1    1 |    * 7200    *    * |    0    0    2    2    1    0    0    0 |   0   0    1    2    2    1    2   0   0    0   0 | 0   1   1    2   1 0
.x ..   .. ..    |   0    2 |    *    * 3600    * |    0    0    2    0    0    2    2    0 |   0   0    2    1    2    0    0   1   2    1   0 | 0   1   2    1   0 1
.. ..   .. .x    |   0    2 |    *    *    * 3600 |    0    0    0    0    1    0    2    2 |   0   0    0    0    2    0    2   0   1    2   1 | 0   0   1    2   1 1
-----------------+----------+---------------------+-----------------------------------------+---------------------------------------------------+---------------------
.. o.5/2x. ..    |   5    0 |    5    0    0    0 | 1440    *    *    *    *    *    *    * |   1   1    0    0    0    1    0   0   0    0   0 | 1   1   0    0   1 0
.. ..   x.3o.    |   3    0 |    3    0    0    0 |    * 1200    *    *    *    *    *    * |   0   2    0    0    0    0    2   0   0    0   0 | 1   0   0    1   2 0
ox ..   .. ..&#x |   1    2 |    0    2    1    0 |    *    * 7200    *    *    *    *    * |   0   0    1    1    1    0    0   0   0    0   0 | 0   1   1    1   0 0
.. ..   xo ..&#x |   2    1 |    1    2    0    0 |    *    *    * 7200    *    *    *    * |   0   0    0    1    0    1    1   0   0    0   0 | 0   1   0    1   1 0
.. ..   .. ox&#x |   1    2 |    0    2    0    1 |    *    *    *    * 3600    *    *    * |   0   0    0    0    2    0    2   0   0    0   0 | 0   0   1    2   1 0
.x5.o   .. ..    |   0    5 |    0    0    5    0 |    *    *    *    *    * 1440    *    * |   0   0    1    0    0    0    0   1   1    0   0 | 0   1   1    0   0 1
.x ..   .. .x    |   0    4 |    0    0    2    2 |    *    *    *    *    *    * 3600    * |   0   0    0    0    1    0    0   0   1    1   0 | 0   0   1    1   0 1
.. ..   .o3.x    |   0    3 |    0    0    0    3 |    *    *    *    *    *    *    * 2400 |   0   0    0    0    0    0    1   0   0    1   1 | 0   0   0    1   1 1
-----------------+----------+---------------------+-----------------------------------------+---------------------------------------------------+---------------------
o.5o.5/2x. ..      12    0 |   30    0    0    0 |   12    0    0    0    0    0    0    0 | 120   *    *    *    *    *    *   *   *    *   * | 1   1   0    0   0 0
.. o.5/2x.3o.      30    0 |   60    0    0    0 |   12   20    0    0    0    0    0    0 |   * 120    *    *    *    *    *   *   *    *   * | 1   0   0    0   1 0
ox5oo   .. ..&#x    1    5 |    0    5    5    0 |    0    0    5    0    0    1    0    0 |   *   * 1440    *    *    *    *   *   *    *   * | 0   1   1    0   0 0
ox ..   xo ..&#x    2    2 |    1    4    1    0 |    0    0    2    2    0    0    0    0 |   *   *    * 3600    *    *    *   *   *    *   * | 0   1   0    1   0 0
ox ..   .. ox&#x    1    4 |    0    4    2    2 |    0    0    2    0    2    0    1    0 |   *   *    *    * 3600    *    *   *   *    *   * | 0   0   1    1   0 0
.. oo5/2xo ..&#x    5    1 |    5    5    0    0 |    1    0    0    5    0    0    0    0 |   *   *    *    *    * 1440    *   *   *    *   * | 0   1   0    0   1 0
.. ..   xo3ox&#x    3    3 |    3    6    0    3 |    0    1    0    3    3    0    0    1 |   *   *    *    *    *    * 2400   *   *    *   * | 0   0   0    1   1 0
.x5.o5/2.o ..       0   12 |    0    0   30    0 |    0    0    0    0    0   12    0    0 |   *   *    *    *    *    *    * 120   *    *   * | 0   1   0    0   0 1
.x5.o   .. .x       0   10 |    0    0   10    5 |    0    0    0    0    0    2    5    0 |   *   *    *    *    *    *    *   * 720    *   * | 0   0   1    0   0 1
.x ..   .o3.x       0    6 |    0    0    3    6 |    0    0    0    0    0    0    3    2 |   *   *    *    *    *    *    *   *   * 1200   * | 0   0   0    1   0 1
.. .o5/2.o3.x       0   12 |    0    0    0   30 |    0    0    0    0    0    0    0   20 |   *   *    *    *    *    *    *   *   *    * 120 | 0   0   0    0   1 1
-----------------+----------+---------------------+-----------------------------------------+---------------------------------------------------+---------------------
o.5o.5/2x.3o.     720    0 | 3600    0    0    0 | 1440 1200    0    0    0    0    0    0 | 120 120    0    0    0    0    0   0   0    0   0 | 1   *   *    *   * *
ox5oo5/2xo ..&#x   12   12 |   30   60   30    0 |   12    0   60   60    0   12    0    0 |   1   0   12   30    0   12    0   1   0    0   0 | * 120   *    *   * *
ox5oo   .. ox&#x    1   10 |    0   10   10    5 |    0    0   10    0    5    2    5    0 |   0   0    2    0    5    0    0   0   1    0   0 | *   * 720    *   * *
ox ..   xo3ox&#x    3    6 |    3   12    3    6 |    0    1    6    6    6    0    3    2 |   0   0    0    3    3    0    2   0   0    1   0 | *   *   * 1200   * *
.. oo5/2xo3ox&#x   30   12 |   60   60    0   30 |   12   20    0   60   30    0    0   20 |   0   1    0    0    0   12   20   0   0    0   1 | *   *   *    * 120 *
.x5.o5/2.o3.x       0 1440 |    0    0 3600 3600 |    0    0    0    0    0 1440 3600 2400 |   0   0    0    0    0    0    0 120 720 1200 120 | *   *   *    *   * 1

© 2004-2019
top of page