Note that the term hexagonal dipyramid in general says nothing about the relative ratio of the edge sizes. An all-unit edged version of the hexagonal dipyramid clearly would be degenerate. This non-degenerate variant uses x-edges at the equator and h-edges for lacings. The triangles {(t,T,T)} then have vertex angles t = arccos(2/3) = 48.189685° resp. T = arccos[1/sqrt(6)] = 65.905157°.

Incidence matrix according to Dynkin symbol

uo oq6oo&zh   → height = 0
                where u = 2 (pseudo)

o. o.6o.    | 2 * |  6 0 |  6  [t6]
.o .o6.o    | * 6 |  2 2 |  4  [T4]
------------+-----+------+---
oo oo6oo&#h | 1 1 | 12 * |  2  h
.. .q ..    | 0 2 |  * 6 |  2  q
------------+-----+------+---
.. oq ..&#h | 1 2 |  2 1 | 12  {(t,T,T)}

uo oq3oq&zh   → height = 0
                where u = 2 (pseudo)

o. o.3o.    | 2 * |  6 0 0 | 3 3  [t6]
.o .o3.o    | * 6 |  2 1 1 | 2 2  [T4]
------------+-----+--------+----
oo oo3oo&#h | 1 1 | 12 * * | 1 1
.. .q ..    | 0 2 |  * 3 * | 2 0
.. .. .q    | 0 2 |  * * 3 | 0 2
------------+-----+--------+----
.. oq ..&#h | 1 2 |  2 1 0 | 6 *  {(t,T,T)}
.. .. oq&#h | 1 2 |  2 0 1 | * 6  {(t,T,T)}