Acronym rad (old: rhode)
Name rhombic dodecahedron,
Voronoi cell of face-centered cubic (fcc) lattice
 
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Inradius sqrt(2/3) = 0.816497
Vertex figure [r4], [R3]
Coordinates
  1. (1, 1, 1)/sqrt(3)     & all permutations, all changes of sign
    (3-fold vertices, inscribed sqrt(4/3)-cube)
  2. (2, 0, 0)/sqrt(3)     & all permutations, all changes of sign
    (4-fold vertices, inscribed sqrt(8/3)-oct)
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dual co
Dihedral angles
(at margins)
  • between {(r,R)2} and {(r,R)2}:   120°
Confer chamfered cube   chamfered oct  
External
links
wikipedia   mathworld

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 according to Dynkin symbol

ao3oo4ob&#zx   → height = 0, 
                 a = rr = sqrt(8/3) = 1.632993, 
                 b = RR = 2/sqrt(3) = 1.154701

o.3o.4o.      | 6 * |  4 |  4  [r4]
.o3.o4.o      | * 8 |  3 |  3  [R3]
--------------+-----+----+---
oo3oo4oo&#x   | 1 1 | 24 |  2
--------------+-----+----+---
.. .. obo&#xt | 2 2 |  4 | 12  {(r,R)2}

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