Acronym ...
Name q3q4x,
Waterman polyhedron number 5 wrt. primitive cubic lattice C3 centered at a hole,
variation of girco
Circumradius sqrt(35)/2 = 2.958040
Coordinates (5/2, 3/2, 1/2)       & all permutations & all changes of sign
Volume 87
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between q . x and q3q:   arccos[-sqrt(2/3)] = 144.735610°
  • between q . x and q4x (at x):   135°
  • between q3q and q4x:   arccos[-1/sqrt(3)] = 125.264390°
Face vector 48, 72, 26
Confer
uniform variant:
girco  
variations:
a3b4c   x3x4q   q3x4x   w3x4x  

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


Incidence matrix according to Dynkin symbol

q3q4x

. . . | 48 |  1  1  1 | 1  1 1
------+----+----------+-------
q . . |  2 | 24  *  * | 1  1 0
. q . |  2 |  * 24  * | 1  0 1
. . x |  2 |  *  * 24 | 0  1 1
------+----+----------+-------
q3q . |  6 |  3  3  0 | 8  * *
q . x |  4 |  2  0  2 | * 12 *
. q4x |  8 |  0  4  4 | *  * 6

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