Acronym	radh
Name	rhombic dodecahedral honeycomb, Voronoi complex of face-centered cubic (fcc) lattice
	©
Vertex figure	cube, q-tet
Dual	octet
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 ⭳ ©  

The vertex set of the rhombic dodecahedral honeycomb is the right shown compound of 2 diamond "lattice"s. In fact already its edge skeleton can be identified by the respective shortest vectors.

The rhombs {(r,R)²} have vertex angles r = arccos(1/3) = 70.528779° resp. R = arccos(-1/3) = 109.471221°. Esp. rr : RR = sqrt(2).

In the above picture the petrol rads belong to this honeycomb, while the white octs just display the relation to the dual one, which is octet, thereby emphasizing the different vertex figures of radh: octs (shown) and tets (gaps).

Incidence matrix

(N → ∞)

  N  * ♦  8 | 12 | 6
  * 2N ♦  4 |  6 | 4
-------+----+----+--
  1  1 | 8N |  3 | 3
-------+----+----+--
  2  2 |  4 | 6N | 2  {(r,R)2}
-------+----+----+--
♦ 6  8 | 24 | 12 | N