Acronym ..., rigfix || sirgaghi
Name (degenerate) rigfix atop sirgaghi
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 || sirgaghi is isomorphic to rofix || sirsashi, thereby interchanging the roles of pentagrams and pentagons, resp. replacing gid by id, peppy by stappy, and stip by pip, resp. rigfix by rofix, sissid || raded by gad || raded, giddip by iddip, and sirgaghi by sirsashi.


Incidence matrix according to Dynkin symbol

ox5oo5/2xx3oo&#x   → height = 0
(rigfix || sirgaghi)

o.5o.5/2o.3o.    | 720    * |   10    5    0    0 |   10    5    5   20   0    0    0    0 |   2   5   1   10   10   10   0    0   0 | 1   2    5   5 0
.o5.o5/2.o3.o    |   * 3600 |    0    1    2    4 |    0    0    2    4   1    4    2    2 |   0   0   1    4    2    2   2    2   1 | 0   2    2   1 1
-----------------+----------+---------------------+----------------------------------------+-----------------------------------------+-----------------
.. ..   x. ..    |   2    0 | 3600    *    *    * |    2    1    0    2   0    0    0    0 |   1   2   0    1    2    2   0    0   0 | 1   1    1   2 0
oo5oo5/2oo3oo&#x |   1    1 |    * 3600    *    * |    0    0    2    4   0    0    0    0 |   0   0   1    4    2    2   0    0   0 | 0   2    2   1 0
.x ..   .. ..    |   0    2 |    *    * 3600    * |    0    0    1    0   1    2    0    0 |   0   0   1    2    0    0   2    1   0 | 0   2    1   0 1
.. ..   .x ..    |   0    2 |    *    *    * 7200 |    0    0    0    1   0    1    1    1 |   0   0   0    1    1    1   1    1   1 | 0   1    1   1 1
-----------------+----------+---------------------+----------------------------------------+-----------------------------------------+-----------------
.. o.5/2x. ..    |   5    0 |    5    0    0    0 | 1440    *    *    *   *    *    *    * |   1   1   0    0    1    0   0    0   0 | 1   1    0   1 0
.. ..   x.3o.    |   3    0 |    3    0    0    0 |    * 1200    *    *   *    *    *    * |   0   2   0    0    0    2   0    0   0 | 1   0    1   2 0
ox ..   .. ..&#x |   1    2 |    0    2    1    0 |    *    * 3600    *   *    *    *    * |   0   0   1    2    0    0   0    0   0 | 0   2    1   0 0
.. ..   xx ..&#x |   2    2 |    1    2    0    1 |    *    *    * 7200   *    *    *    * |   0   0   0    1    1    1   0    0   0 | 0   1    1   1 0
.x5.o   .. ..    |   0    5 |    0    0    5    0 |    *    *    *    * 720    *    *    * |   0   0   1    0    0    0   2    0   0 | 0   2    0   0 1
.x ..   .x ..    |   0    4 |    0    0    2    2 |    *    *    *    *   * 3600    *    * |   0   0   0    1    0    0   1    1   0 | 0   1    1   0 1
.. .o5/2.x ..    |   0    5 |    0    0    0    5 |    *    *    *    *   *    * 1440    * |   0   0   0    0    1    0   1    0   1 | 0   1    0   1 1
.. ..   .x3.o    |   0    3 |    0    0    0    3 |    *    *    *    *   *    *    * 2400 |   0   0   0    0    0    1   0    1   1 | 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
.. o.5/2x.3o.      30    0 |   60    0    0    0 |   12   20    0    0   0    0    0    0 |   * 120   *    *    *    *   *    *   * | 1   0    0   1 0
ox5oo   .. ..&#x    1    5 |    0    5    5    0 |    0    0    5    0   1    0    0    0 |   *   * 720    *    *    *   *    *   * | 0   2    0   0 0
ox ..   xx ..&#x    2    4 |    1    4    2    2 |    0    0    2    2   0    1    0    0 |   *   *   * 3600    *    *   *    *   * | 0   1    1   0 0
.. oo5/2xx ..&#x    5    5 |    5    5    0    5 |    1    0    0    5   0    0    1    0 |   *   *   *    * 1440    *   *    *   * | 0   1    0   1 0
.. ..   xx3oo&#x    3    3 |    3    3    0    3 |    0    1    0    3   0    0    0    1 |   *   *   *    *    * 2400   *    *   * | 0   0    1   1 0
.x5.o5/2.x ..       0   60 |    0    0   60   60 |    0    0    0    0  12   30   12    0 |   *   *   *    *    *    * 120    *   * | 0   1    0   0 1
.x ..   .x3.o       0    6 |    0    0    3    6 |    0    0    0    0   0    3    0    2 |   *   *   *    *    *    *   * 1200   * | 0   0    1   0 1
.. .o5/2.x3.o       0   30 |    0    0    0   60 |    0    0    0    0   0    0   12   20 |   *   *   *    *    *    *   *    * 120 | 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 | 1   *    *   * *
ox5oo5/2xx ..&#x   12   60 |   30   60   60   60 |   12    0   60   60  12   30   12    0 |   1   0  12   30   12    0   1    0   0 | * 120    *   * *
ox ..   xx3oo&#x    3    6 |    3    6    3    6 |    0    1    3    6   0    3    0    2 |   0   0   0    3    0    2   0    1   0 | *   * 1200   * *
.. oo5/2xx3oo&#x   30   30 |   60   30    0   60 |   12   20    0   60   0    0   12   20 |   0   1   0    0   12   20   0    0   1 | *   *    * 120 *
.x5.o5/2.x3.o       0 3600 |    0    0 3600 7200 |    0    0    0    0 720 3600 1440 2400 |   0   0   0    0    0    0 120 1200 120 | *   *    *   * 1

© 2004-2019
top of page