Acronym rad (old: rhode)
Name rhombic dodecahedron,
Voronoi cell of face-centered cubic (fcc) lattice,
terminally chamfered cube,
terminally chamfered octahedron,
surtegmated cube,
surtegmated octahedron
 
 © ©
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).

All a and b edges, provided in the below description, only qualify as pseudo edges wrt. the full polyhedron. Edge size used here is rR = x = 1.


Incidence matrix according to Dynkin symbol

o3m4o =
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
-------------+-----+----+---
ao .. ob&#zx | 2 2 |  4 | 12  {(r,R)2}

m3o3m =
aoo3oao3ooa&#zx   → height = 0
                    a = rr = sqrt(8/3) = 1.632993

o..3o..3o..     | 4 * * |  3  0 |  3  [R3]
.o.3.o.3.o.     | * 6 * |  2  2 |  4  [r4]
..o3..o3..o     | * * 4 |  0  3 |  3  [R3]
----------------+-------+-------+---
oo.3oo.3oo.&#x  | 1 1 0 | 12  * |  2
.oo3.oo3.oo&#x  | 0 1 1 |  * 12 |  2
----------------+-------+-------+---
... oao ...&#xt | 1 2 1 |  2  2 | 12  {(r,R)2}

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