Acronym	...
Name	trapezo-rhombic dodecahedron, Voronoi cell of hexagonal close-packing (hcp) "lattice"
	©
Inradius	sqrt(2/3) = 0.816497
Vertex figure	[r4], [R3]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dual	tobcu
Dihedral angles (at margins)	between {(r,R)2} and {(r,R)2}:   120° between {(r,R)2} and {(r2,R2)}:   120° between {(r2,R2)} and {(r2,R2)} (at RRtrapezium-edge):   120° between {(r2,R2)} and {(r2,R2)} (at rrtrapezium-edge):   120°
Face vector	14, 24, 12
Confer	related polyhedra: rad
External links

The rhombs {(r,R)²} have vertex angles r = arccos(1/3) = 70.528779° resp. R = arccos(-1/3) = 109.471221°. Esp. rr_rhomb : RR_rhomb = sqrt(2). Its side length (rR-edge) used here is rR = x = 1. The trapezia {(r²,R²)} have the same vertex angles. Its other, non-rR-edge side lengths have sizes RR_trapezium = y = 2/3 and rr_trapezium = z = 4/3.

Note, that if the axially top-most bistratic layer gets rotated by 60°, then the result would become rad. In fact this simply is because this polyhedron here is the dual of tobcu, while that outcome would be the dual of the respectively gyrated bicupola, i.e. co.

Incidence matrix according to Dynkin symbol

oaooao3ooaaoo&#(x,x,y,x,x)t   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/3
                                height(3,4) = y = RRtrapezium = 2/3 (short trapezium side)
                                a = rrrhomb = sqrt(8/3) = 1.632993 (long rhomb-diagonal)
                                z = 2y = rrtrapezium = 4/3 (long trapezium side)

o.....3o.....             | 1 * * * * * | 3 0 0 0 0 0 | 3 0 0  [R3]
.o....3.o....             | * 3 * * * * | 1 2 1 0 0 0 | 2 2 0  [r4]
..o...3..o...             | * * 3 * * * | 0 2 0 1 0 0 | 1 2 0  [R3]
...o..3...o..             | * * * 3 * * | 0 0 0 1 2 0 | 0 2 1  [R3]
....o.3....o.             | * * * * 3 * | 0 0 1 0 2 1 | 0 2 2  [r4]
.....o3.....o             | * * * * * 1 | 0 0 0 0 0 3 | 0 0 3  [R3]
--------------------------+-------------+-------------+------
oo....3oo....&#x          | 1 1 0 0 0 0 | 3 * * * * * | 2 0 0  x
.oo...3.oo...&#x          | 0 1 1 0 0 0 | * 6 * * * * | 1 1 0  x
.o..o.3.o..o.&#z          | 0 1 0 0 1 0 | * * 3 * * * | 0 2 0  z
..oo..3..oo..&#y          | 0 0 1 1 0 0 | * * * 3 * * | 0 2 0  y
...oo.3...oo.&#x          | 0 0 0 1 1 0 | * * * * 6 * | 0 1 1  x
....oo3....oo&#x          | 0 0 0 0 1 1 | * * * * * 3 | 0 0 2  x
--------------------------+-------------+-------------+------
oao... ......&#xt         | 1 2 1 0 0 0 | 2 2 0 0 0 0 | 3 * *  {(r,R)2}
.oooo.3.oooo.&#(y,x,z,x)r | 0 1 1 1 1 0 | 0 1 1 1 1 0 | * 6 *  {(r2,R2)}
...oao ......&#xt         | 0 0 0 1 2 1 | 0 0 0 0 2 2 | * * 3  {(r,R)2}

or
o.....3o.....            & | 2 * * | 3  0 0 0 | 3 0  [R3]
.o....3.o....            & | * 6 * | 1  2 1 0 | 2 2  [r4]
..o...3..o...            & | * * 6 | 0  2 0 1 | 1 2  [R3]
---------------------------+-------+----------+----
oo....3oo....&#x         & | 1 1 0 | 6  * * * | 2 0  x
.oo...3.oo...&#x         & | 0 1 1 | * 12 * * | 1 1  x
.o..o.3.o..o.&#z           | 0 2 0 | *  * 3 * | 0 2  z
..oo..3..oo..&#y           | 0 0 2 | *  * * 3 | 0 2  y
---------------------------+-------+----------+----
oao... ......&#xt        & | 1 2 1 | 2  2 0 0 | 6 *  {(r,R)2}
.oooo.3.oooo.&#(y,x,z,x)r  | 0 2 2 | 0  2 1 1 | * 6  {(r2,R2)}