Acronym ...
Name x3x4q,
variation of great rhombicuboctahedron,
Waterman polyhedron number 7 wrt. face-centered cubic lattice A3 centered at a lattice point
  
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Circumradius sqrt(7) = 2.645751
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x . q and x3x:   arccos[-sqrt(2/3)] = 144.735610°
  • between x . q and x4q (at q):   135°
  • between x3x and x4q:   arccos[-1/sqrt(3)] = 125.264390°
Face vector 48, 72, 26
Confer
uniform variant:
girco  
variations:
a3b4c   q3x4x   q3q4x   w3x4x  

using edge sizes x = 1 and q = sqrt(2) = 1.414214


Incidence matrix according to Dynkin symbol

x3x4q

. . . | 48 |  1  1  1 | 1  1 1
------+----+----------+-------
x . . |  2 | 24  *  * | 1  1 0
. x . |  2 |  * 24  * | 1  0 1
. . q |  2 |  *  * 24 | 0  1 1
------+----+----------+-------
x3x . |  6 |  3  3  0 | 8  * *
x . q |  4 |  2  0  2 | * 12 *
. x4q |  8 |  0  4  4 | *  * 6

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