Acronym ...
Name q3x3o,
variation of truncated tetrahedron,
triangle-snub small rhombicuboctahedron
 
Circumradius sqrt[5+2 sqrt(2)]/2 = 1.398966
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x3o and q3x:   arccos(-1/3) = 109.471221°
  • between q3x and q3x (at q):   arccos(1/3) = 70.528779°
Face vector 12, 18, 8
Confer
uniform variant:
tut  
variations:
a3b3c   x3v3o   x3q3o   x3u3o   x3w3o   v3x3o   u3x3o   w3x3o   (-x)3x3o  

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

This polyhedron can be vertex inscribed into sirco. In fact, the latter is just a tegum sum of 2 such in dual position. Conversely it can be derived from sirco by means of a mere alternated faceting, cf. the above picture.


Incidence matrix according to Dynkin symbol

q3x3o

. . . | 12 | 1  2 | 2 1
------+----+------+----
q . . |  2 | 6  * | 2 0
. x . |  2 | * 12 | 1 1
------+----+------+----
q3x . |  6 | 3  3 | 4 *
. x3o |  3 | 0  3 | * 4

o3/2x3q

.   . . | 12 |  2 1 | 1 2
--------+----+------+----
.   x . |  2 | 12 * | 1 1
.   . q |  2 |  * 6 | 0 2
--------+----+------+----
o3/2x . |  3 | 3  0 | 4 *
.   x3q |  6 | 3  3 | * 4

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