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Acronym	chic
Name	chamferedcube, octahedrally truncatedrhombic dodecahedron
	©  ©
Vertex figure	[4,H2], [h3]
Coordinates	(1/2 + 1/sqrt(3), 1/2 + 1/sqrt(3), 1/2 + 1/sqrt(3))       & all changes of sign (vertex inscribedcube) (1/2, 1/2, 1/2 + 2/sqrt(3))               & all permutations, all changes of sign
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles (at margins)	between {4} and {(h,H,H)2}:   135° between {(h,H,H)2} and {(h,H,H)2}:   120°
Face vector	32, 48, 18
Confer	rad  cube  oq3oo4ux&zc
External links

The non-regular hexagons {(h,H,H)²} have vertex angles h = arccos(-1/3) = 109.471221° resp. H = arccos[-1/sqrt(3)] = 125.264390°.

Octahedral truncation applies to the octahedral vertices (vertex inscribedoct) only. Wrt. therad thisproduces new square faces there. These are then face planes of a cuttingcube. – The above transition shows a dynamical mutual scaling ofcube andrad.The chamfered cube then is the instance, where all edges happen to have the same length.However there also occurs a not so deep truncation as theWaterman polyhedron number 5 wrt. body-centered cubiclattice C₃* centered at a lattice point (oq3oo4ux&#zc).(Note that here the diagonals of the non-regular hexagons will not be side-parallel, while there they happen to be.)

Chamfering (or edge-only beveling – here is being applied to thecube) flatens the former edges into new (non-regular hexagonal) faces.There is a deeper, terminal chamfering of thecube too, which then reduces the original faces to nothing. Then the hexagons will become rhombs and the total figure becomes therad.–When considering the below providedtegum sumDynkin symbol, it becomes obvious that this figure also can be seen as aStott expansion of therad.

Incidence matrix according toDynkin symbol

ax4oo3oc&#zx   → height = 0                 a = (3+2 sqrt(3))/3 = 2.154701                 c = sqrt(8/3) = 1.632993(tegum sum of a-cube and (x,c)-sirco)o.4o.3o.     | 8  * |  3  0 |  3 0  [h3].o4.o3.o     | * 24 |  1  2 |  2 1  [4,H2]-------------+------+-------+-----oo4oo3oo&#x  | 1  1 | 24  * |  2 0.x .. ..     | 0  2 |  * 24 |  1 1-------------+------+-------+-----ax .. oc&#zx | 2  4 |  4  2 | 12 *  {(h,H,H)2}.x4.o ..     | 0  4 |  0  4 |  * 6  {4}