Acronym gabric
Name great birhombatotetracontoctachoron
Circumradius sqrt[a2 + 2 sqrt(2) ab + 3b2]
Confer
variants:
case 0 < b:a < 1/2 / case b:a = 1/2 / case 1/2 < b:a < 2+sqrt(2) / case b:a = 2+sqrt(2) / this case 2+sqrt(2) < b:a < ∞
general polytopal classes:
isogonal  
External
links
polytopewiki

This polychoron is the general form of one of the 3 phases of the tegum sum of 2 inverted general srico variants, ao3ob4bo3oa&#zc, here in fact the realm of 2+sqrt(2) < b:a < ∞. The other ones will be sabric for 0 < b:a < 1/2 resp. mabric for 1/2 < b:a < 2+sqrt(2).

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 2+sqrt(2) (recont) and b:a → ∞ (bamic) respectively.


Incidence matrix according to Dynkin symbol

ao3ob4bo3oa&#zc   → height = 0
                    c = sqrt[(2-sqrt(2)) a2 - (6-4 sqrt(2)) ab + (6-4 sqrt(2)) b2]
                    2+sqrt(2) < b:a < ∞

o.3o.4o.3o.     & | 576 |   2    4    4 |   1   4   2    6    6 |  2   5   2   2
------------------+-----+---------------+-----------------------+---------------
a. .. .. ..     & |   2 | 576    *    * |   1   2   0    2    0 |  2   2   1   0
.. .. b. ..     & |   2 |   * 1152    * |   0   1   1    0    1 |  1   1   0   1
oo3oo4oo3oo&#c    |   2 |   *    * 1152 |   0   0   0    2    2 |  0   2   1   1
------------------+-----+---------------+-----------------------+---------------
a.3o. .. ..     & |   3 |   3    0    0 | 192   *   *    *    * |  2   0   0   0
a. .. b. ..     & |   4 |   2    2    0 |   * 576   *    *    * |  1   1   0   0
.. o.4b. ..     & |   4 |   0    4    0 |   *   * 288    *    * |  1   0   0   1
ao .. .. ..&#c  & |   3 |   1    0    2 |   *   *   * 1152    * |  0   1   1   0
.. ob .. ..&#c  & |   3 |   0    1    2 |   *   *   *    * 1152 |  0   1   0   1
------------------+-----+---------------+-----------------------+---------------
a.3o.4b. ..     & |  24 |  24   24    0 |   8  12   6    0    0 | 48   *   *   *  (a,b)-sirco variant
ao .. bo ..&#c  & |   5 |   2    2    4 |   0   1   0    2    2 |  * 576   *   *  (a,b,c)-squippy variant
ao .. .. oa&#c    |   4 |   2    0    4 |   0   0   0    4    0 |  *   * 288   *  tetragonal disphenoid (tet variant)
.. ob4bo ..&#c    |   8 |   0    8    8 |   0   0   2    0    8 |  *   *   * 144  squap variant

© 2004-2021
top of page