Acronym sabric
Name small birhombatotetracontoctachoron
Circumradius sqrt[a2 + 2 sqrt(2) ab + 3b2]
Confer
variants:
this 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) / 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 0 < b:a < 1/2. The other ones will be mabric for 1/2 < b:a < 2+sqrt(2) resp. gabric for 2+sqrt(2) < b:a < ∞.

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 0 (bicont) and b:a = 1/2 (respic) respectively. While the latter limit is seen quite direct, in the former process of b → 0 one observes the followings: the b-coes clearly vanish by size, the corresponding vertices will coincide by 12; the square antiprisms ob4bo&#c then become an 8 fold coincident single edge; but the a-base connected pairs of triangular antipodia ao3ob&#c, instead of becoming according triangular pyramids each, rather happen to swap into rosettes of 3 further disphenoids.


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]
                    0 < b:a < 1/2

o.3o.4o.3o.     & | 576 |   2    4    4 |   1   2   2    6    6 |  1   4   2   2
------------------+-----+---------------+-----------------------+---------------
a. .. .. ..     & |   2 | 576    *    * |   1   0   0    2    0 |  0   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   *   *    *    * |  0   2   0   0
.. o.4b. ..     & |   4 |   0    4    0 |   * 288   *    *    * |  1   0   0   1
.. .. b.3o.     & |   3 |   0    3    0 |   *   * 384    *    * |  1   1   0   0
ao .. .. ..&#c  & |   3 |   1    0    2 |   *   *   * 1152    * |  0   1   1   0
.. ob .. ..&#c  & |   3 |   0    1    2 |   *   *   *    * 1152 |  0   1   0   1
------------------+-----+---------------+-----------------------+---------------
.. o.4b.3o.     & |  12 |   0   24    0 |   0   6   8    0    0 | 48   *   *   * b-co
ao3ob .. ..&#c  & |   6 |   3    3    6 |   1   0   1    3    3 |  * 384   *   * triangular antipodium
ao .. .. oa&#c    |   4 |   2    0    4 |   0   0   0    4    0 |  *   * 288   * tetragonal disphenoid
.. ob4bo ..&#c    |   8 |   0    8    8 |   0   2   0    0    8 |  *   *   * 144 square antiprism

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