Acronym	...
Name	dual of hexagonal prism, hexgonal dipyramid
	©
Vertex figure	[t6], [T4]
Dihedral angles	at long edge:   arccos(-3/5) = 126.869898° at short edge:   arccos(-3/5) = 126.869898°
Dual	hexagonal prism
Face vector	8, 18, 12
Confer	more general: m mNo   variations: uo oq6oo&#zh   general polytopal classes: Catalan polyhedra
External links

The triangles {(t,T,T)} have vertex angles t = arccos(7/8) = 28.955024° resp. T = arccos(1/4) = 75.522488°.

Note that the term hexagonal dipyramid in general says nothing about the relative ratio of the edge sizes. Here the edge ratio is chosen such as to match their duality to the hexagonal prism.

Incidence matrix according to Dynkin symbol

m m6o =
oxo6ooo&#ut   → both heights = sqrt(3) = 1.732051

o..6o..    | 1 * * | 6 0 0 | 6 0  [t6]
.o.6.o.    | * 6 * | 1 2 1 | 2 2  [T4]
..o6..o    | * * 1 | 0 0 6 | 0 6  [t6]
-----------+-------+-------+----
oo.6oo.&#u | 1 1 0 | 6 * * | 2 0  u
.x. ...    | 0 2 0 | * 6 * | 1 1  x
.oo6.oo&#u | 0 1 1 | * * 6 | 0 2  u
-----------+-------+-------+----
ox. ...&#u | 1 2 0 | 2 1 0 | 6 *  {(t,T,T)}
.xo ...&#u | 0 2 1 | 0 1 2 | * 6  {(t,T,T)}

m m6o =
ao ox6oo&#zu   → height = 0
                   a = sqrt(12) = 3.464102

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