Acronym	bautic, J67
Name	biaugmented truncated cube
	© ©
Vertex figures	[3,43], [3,4,3,8], [3,82]
Lace city in approx. ASCII-art	o q o x w w x w w w w x w w x o q o
	x x x w w x o U o (U=qw=u+q=x+w) o U o x w w x x x
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {4} (at join):   arccos(-sqrt[(3+2 sqrt(2))/6]) = 170.264390° between {3} and {4} (at squacu lacings):   arccos[-sqrt(2/3)] = 144.735610° between {3} and {8} (at join):   arccos[-sqrt(2/3)] = 144.735610° between {3} and {8} (at tic edges):   arccos[-1/sqrt(3)] = 125.264390° between {8} and {8}:   90°
Face vector	32, 60, 30
Confer	uniform relative: tic   related Johnson solids: squacu   autic   general polytopal classes: Johnson solids
External links

Incidence matrix according to Dynkin symbol

xxooxx4oxwwxo&#xt   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
                  height(3,4) = 1

o.....4o.....     | 4 * * * * * | 2 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0  top polar
.o....4.o....     | * 8 * * * * | 0 1 1 1 1 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0  upper join
..o...4..o...     | * * 4 * * * | 0 0 0 0 2 1 0 0 0 0 0 | 0 0 0 1 2 0 0 0 0  upper tropal
...o..4...o..     | * * * 4 * * | 0 0 0 0 0 1 2 0 0 0 0 | 0 0 0 0 2 1 0 0 0  lower tropal
....o.4....o.     | * * * * 8 * | 0 0 0 0 0 0 1 1 1 1 0 | 0 0 0 0 1 1 1 1 0  lower join
.....o4.....o     | * * * * * 4 | 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 1 2 1  bottom polar
------------------+-------------+-----------------------+------------------
x..... ......     | 2 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 0 0 0 0
oo....4oo....&#x  | 1 1 0 0 0 0 | * 8 * * * * * * * * * | 0 1 1 0 0 0 0 0 0
.x.... ......     | 0 2 0 0 0 0 | * * 4 * * * * * * * * | 0 1 0 1 0 0 0 0 0
...... .x....     | 0 2 0 0 0 0 | * * * 4 * * * * * * * | 0 0 1 0 1 0 0 0 0
.oo...4.oo...&#x  | 0 1 1 0 0 0 | * * * * 8 * * * * * * | 0 0 0 1 1 0 0 0 0
..oo..4..oo..&#x  | 0 0 1 1 0 0 | * * * * * 4 * * * * * | 0 0 0 0 2 0 0 0 0
...oo.4...oo.&#x  | 0 0 0 1 1 0 | * * * * * * 8 * * * * | 0 0 0 0 1 1 0 0 0
...... ....x.     | 0 0 0 0 2 0 | * * * * * * * 4 * * * | 0 0 0 0 1 0 1 0 0
....x. ......     | 0 0 0 0 2 0 | * * * * * * * * 4 * * | 0 0 0 0 0 1 0 1 0
....oo4....oo&#x  | 0 0 0 0 1 1 | * * * * * * * * * 8 * | 0 0 0 0 0 0 1 1 0
.....x ......     | 0 0 0 0 0 2 | * * * * * * * * * * 4 | 0 0 0 0 0 0 0 1 1
------------------+-------------+-----------------------+------------------
x.....4o.....     | 4 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * *  top {4}
xx.... ......&#x  | 2 2 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 | * 4 * * * * * * *  augmenting {4}
...... ox....&#x  | 1 2 0 0 0 0 | 0 2 0 1 0 0 0 0 0 0 0 | * * 4 * * * * * *  augmenting {3}
.xo... ......&#x  | 0 2 1 0 0 0 | 0 0 1 0 2 0 0 0 0 0 0 | * * * 4 * * * * *  upper {3}
...... .xwwx.&#xt | 0 2 2 2 2 0 | 0 0 0 1 2 2 2 1 0 0 0 | * * * * 4 * * * *  {8}
...ox. ......&#x  | 0 0 0 1 2 0 | 0 0 0 0 0 0 2 0 1 0 0 | * * * * * 4 * * *  lower {3}
...... ....xo&#x  | 0 0 0 0 2 1 | 0 0 0 0 0 0 0 1 0 2 0 | * * * * * * 4 * *  augmenting {3}
....xx ......&#x  | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * 4 *  augmenting {4}
.....x4.....o     | 0 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * 1  bottom {4}

or
o.....4o.....     & | 8  * * | 2  2 0 0  0 0 | 1 2 1 0 0  polar
.o....4.o....     & | * 16 * | 0  1 1 1  1 0 | 0 1 1 1 1  join
..o...4..o...     & | *  * 8 | 0  0 0 0  2 1 | 0 0 0 1 2  tropal
--------------------+--------+---------------+----------
x..... ......     & | 2  0 0 | 8  * * *  * * | 1 1 0 0 0
oo....4oo....&#x  & | 1  1 0 | * 16 * *  * * | 0 1 1 0 0
.x.... ......     & | 0  2 0 | *  * 8 *  * * | 0 1 0 1 0
...... .x....     & | 0  2 0 | *  * * 8  * * | 0 0 1 0 1
.oo...4.oo...&#x  & | 0  1 1 | *  * * * 16 * | 0 0 0 1 1
..oo..4..oo..&#x    | 0  0 2 | *  * * *  * 4 | 0 0 0 0 2
--------------------+--------+---------------+----------
x.....4o.....     & | 4  0 0 | 4  0 0 0  0 0 | 2 * * * *  polar {4}
xx.... ......&#x  & | 2  2 0 | 1  2 1 0  0 0 | * 8 * * *  augmenting {4}
...... ox....&#x  & | 1  2 0 | 0  2 0 1  0 0 | * * 8 * *  augmenting {3}
.xo... ......&#x  & | 0  2 1 | 0  0 1 0  2 0 | * * * 8 *  medial {3}
...... .xwwx.&#xt   | 0  4 4 | 0  0 0 2  4 2 | * * * * 4  {8}