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

The vertex set of the rhombic dodecahedral honeycomb is a 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).


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

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