Acronym	gabred
Name	great birhombatodecachoron
Net	©
Circumradius	sqrt[(2a2+2ab+3b2)/5]
Face vector	60, 300, 360, 120
Confer	variants: case 0 < b:a < 1/2 / case b:a = 1/2 / case 1/2 < b:a < 3 / case b:a = 3 / this case 3 < b:a < ∞ general polytopal classes: isogonal
External links

This polychoron is the general form of one of the 3 phases of the tegum sum of 2 inverted general srip variants, ao3ob3bo3oa&#zc, here in fact the realm of 3 < b:a < ∞. The other ones will be sabred for 0 < b:a < 1/2 resp. mabred for 1/2 < b:a < 3.

Further there are singular transition cases too. The relevant ones for the current realm are the bordering cases b:a = 3 (redeca) and b:a → ∞ (apid) respectively.

Incidence matrix according to Dynkin symbol

ao3ob3bo3oa&#zc   → height = 0
                    c = sqrt[(3a2-2ab+2b2)/5]
                    3 < b:a < ∞

o.3o.3o.3o.     & | 60 |  2   4   4 |  1  4  2   6   6 |  2  5  2  2
------------------+----+------------+------------------+------------
a. .. .. ..     & |  2 | 60   *   * |  1  2  0   2   0 |  2  2  1  0
.. .. b. ..     & |  2 |  * 120   * |  0  1  1   0   1 |  1  1  0  1
oo3oo3oo3oo&#c    |  2 |  *   * 120 |  0  0  0   2   2 |  0  2  1  1
------------------+----+------------+------------------+------------
a.3o. .. ..     & |  3 |  3   0   0 | 20  *  *   *   * |  2  0  0  0
a. .. b. ..     & |  4 |  2   2   0 |  * 60  *   *   * |  1  1  0  0
.. o.3b. ..     & |  3 |  0   3   0 |  *  * 40   *   * |  1  0  0  1
ao .. .. ..&#c  & |  3 |  1   0   2 |  *  *  * 120   * |  0  1  1  0
.. ob .. ..&#c  & |  3 |  0   1   2 |  *  *  *   * 120 |  0  1  0  1
------------------+----+------------+------------------+------------
a.3o.3b. ..     & | 12 | 12  12   0 |  4  6  4   0   0 | 10  *  *  *  small rhombitetratetrahedron (co variant)
ao .. bo ..&#c  & |  5 |  2   2   4 |  0  1  0   2   2 |  * 60  *  *  rectangular pyramid (squippy variant)
ao .. .. oa&#c    |  4 |  2   0   4 |  0  0  0   4   0 |  *  * 30  *  tetragonal disphenoid (tet variant)
.. ob3bo ..&#c    |  6 |  0   6   6 |  0  0  2   0   6 |  *  *  * 20  triangular antiprism (oct variant)