Acronym gabirch
Name great birhombatocubic honeycomb
Confer
variants:
case 0 < b:a < 1/sqrt(2) / case b:a = 1/sqrt(2) / case 1/sqrt(2) < b:a < 3/sqrt(2) / case b:a = 3/sqrt(2) / this case 3/sqrt(2) < b:a < ∞
general polytopal classes:
isogonal  

This honeycomb is the general form of one of the 3 phases of the tegum sum of 2 inverted general srich variants, ao4ob3bo4oa&#zc, here in fact the realm of 3/sqrt(2) < b:a < ∞. The other ones will be sabirch for 0 < b:a < 1/sqrt(2) resp. mabirch for 1/sqrt(2) < b:a < 3/sqrt(2).

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 3/sqrt(2) (rebatch) and b:a → ∞ (bamich) respectively.


Incidence matrix according to Dynkin symbol

ao4ob3bo4oa&#zc   (N → ∞)   → height = 0
                              c = sqrt[3a2-2ab sqrt(2)+2b2]/2
                              3/sqrt(2) < b:a < ∞

o.4o.3o.4o.     & | 12N |   2   4   4 |  1   4  2   6   6 | 2   5  2  2
------------------+-----+-------------+-------------------+------------
a. .. .. ..     & |   2 | 12N   *   * |  1   2  0   2   0 | 2   2  1  0
.. .. b. ..     & |   2 |   * 24N   * |  0   1  1   0   1 | 1   1  0  1
oo4oo3oo4oo&#c    |   2 |   *   * 24N |  0   0  0   2   2 | 0   2  1  1
------------------+-----+-------------+-------------------+------------
a.4o. .. ..     & |   4 |   4   0   0 | 3N   *  *   *   * | 2   0  0  0
a. .. b. ..     & |   4 |   2   2   0 |  * 12N  *   *   * | 1   1  0  0
.. o.3b. ..     & |   3 |   0   3   0 |  *   * 8N   *   * | 1   0  0  1
ao .. .. ..&#c  & |   3 |   1   0   2 |  *   *  * 24N   * | 0   1  1  0
.. ob .. ..&#c  & |   3 |   0   1   2 |  *   *  *   * 24N | 0   1  0  1
------------------+-----+-------------+-------------------+------------
a.4o.3b. ..     & |  24 |  24  24   0 |  6  12  8   0   0 | N   *  *  *  rhombicuboctahedron (sirco variant)
ao .. bo ..&#c  & |   5 |   2   2   4 |  0   1  0   2   2 | * 12N  *  *  rectangular pyramid (squippy variant)
ao .. .. oa&#c    |   4 |   2   0   4 |  0   0  0   4   0 | *   * 6N  *  tetragonal disphenoid (tet variant)
.. ob3bo ..&#c    |   6 |   0   6   6 |  0   0  2   0   6 | *   *  * 4N  triangular antiprism (oct variant)

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