Acronym	sabric
Name	small birhombatotetracontoctachoron
	©
Circumradius	sqrt[a2 + 2 sqrt(2) ab + 3b2]
Face vector	576, 2880, 3168, 864
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
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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.

The above picture displays the .. o.4b.3o. in green (note that the square first ones are highly deformed in their nearly tangential representation) and the ao .. .. oa&#c in red. While the ao3ob .. ..&#c and .. bo4ob ..&#c are left blank in order to get a view into this structure.

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