q3x3o

Acronym	...
Name	q3x3o, variation of truncated tetrahedron, triangle-snub small rhombicuboctahedron
VRML	⭳
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

x3o4s

demi( . . . ) | 12 | 1  2 | 1 2
--------------+----+------+----
      . o4s ) ♦  2 | 6  * | 0 2  q
demi( x . . ) |  2 | * 12 | 1 1
--------------+----+------+----
demi( x3o . ) |  3 | 0  3 | 4 *
sefa( x3o4s ) |  6 | 3  3 | * 4

starting figure: x3o4x

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