Acronym hixacube
Name hix atop edge-parallel cube
Circumradius sqrt(3)/2 = 0.866025
Lace hyper city
in approx. ASCII-art
o x o       o o x
      x o o      
                 
                 
                 
                 
      x x x      
I.e. a regular tetrahedron in position space of 3 mutually orthogonal lines resp. their Minkowski sum (a cube) within object space.
Confer
uniform relative:
hax  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xoox oxox ooxx&#x   → all pairwise heights = 1/sqrt(2) = 0.707107
                      height(123,4) = 1/sqrt(3) = 0.577350
(hix || edge-para cube)

o... o... o...    & | 6 * | 1  4  4  0 |  6 4  4  4  8 0 | 2  8  4 1 4 12  4 0 | 5 1  8 4  6 | 1 2 5
...o ...o ...o      | * 8 | 0  0  3  3 |  0 0  3  6  3 3 | 0  0  6 3 1  6  3 1 | 0 3  3 3  6 | 0 3 3
--------------------+-----+------------+-----------------+---------------------+-------------+------
x... .... ....    & | 2 0 | 3  *  *  * |  4 0  4  0  0 0 | 2  4  4 0 0  8  0 0 | 4 1  4 4  4 | 1 2 4
oo.. oo.. oo..&#x & | 2 0 | * 12  *  * |  2 2  0  0  2 0 | 1  5  0 0 2  4  1 0 | 4 0  5 2  2 | 1 1 4
o..o o..o o..o&#x & | 1 1 | *  * 24  * |  0 0  1  2  2 0 | 0  0  2 1 1  4  2 0 | 0 1  3 2  4 | 0 2 3
...x .... ....    & | 0 2 | *  *  * 12 |  0 0  1  2  0 2 | 0  0  4 2 0  2  1 1 | 0 3  1 2  4 | 0 3 2
--------------------+-----+------------+-----------------+---------------------+-------------+------
xo.. .... ....&#x & | 3 0 | 1  2  0  0 | 12 *  *  *  * * | 1  2  0 0 0  2  0 0 | 3 0  2 2  1 | 1 1 3
ooo. ooo. ooo.&#x   | 3 0 | 0  3  0  0 |  * 8  *  *  * * | 0  3  0 0 1  0  0 0 | 3 0  3 0  0 | 1 0 3
x..x .... ....&#x & | 2 2 | 1  0  2  1 |  * * 12  *  * * | 0  0  2 0 0  2  0 0 | 0 1  1 2  2 | 0 2 2
.... o..x ....&#x & | 1 2 | 0  0  2  1 |  * *  * 24  * * | 0  0  1 1 0  1  1 0 | 0 1  1 1  3 | 0 2 2
oo.o oo.o oo.o&#x & | 2 1 | 0  1  2  0 |  * *  *  * 24 * | 0  0  0 0 1  2  1 0 | 0 0  3 1  2 | 0 1 3
...x ...x ....    & | 0 4 | 0  0  0  4 |  * *  *  *  * 6 | 0  0  2 1 0  0  0 1 | 0 3  0 1  2 | 0 3 1
--------------------+-----+------------+-----------------+---------------------+-------------+------
xo.. ox.. ....&#x &  4 0 | 2  4  0  0 |  4 0  0  0  0 0 | 3  *  * * *  *  * * | 2 0  0 2  0 | 1 1 2
xoo. .... ....&#x &  4 0 | 1  5  0  0 |  2 2  0  0  0 0 | * 12  * * *  *  * * | 2 0  1 0  0 | 1 0 2
x..x o..x ....&#x &  2 4 | 1  0  4  4 |  0 0  2  2  0 1 | *  * 12 * *  *  * * | 0 1  0 1  1 | 0 2 1
.... o..x o..x&#x &  1 4 | 0  0  4  4 |  0 0  0  4  0 1 | *  *  * 6 *  *  * * | 0 1  0 0  2 | 0 2 1
oooo oooo oooo&#x    3 1 | 0  3  3  0 |  0 1  0  0  3 0 | *  *  * * 8  *  * * | 0 0  3 0  0 | 0 0 3
xo.x .... ....&#x &  3 2 | 1  2  4  1 |  1 0  1  1  2 0 | *  *  * * * 24  * * | 0 0  1 1  1 | 0 1 2
.... .... oo.x&#x &  2 2 | 0  1  4  1 |  0 0  0  2  2 0 | *  *  * * *  * 12 * | 0 0  1 0  2 | 0 1 2
...x ...x ...x       0 8 | 0  0  0 12 |  0 0  0  0  0 6 | *  *  * * *  *  * 1 | 0 3  0 0  0 | 0 3 0
--------------------+-----+------------+-----------------+---------------------+-------------+------
xoo. oxo. ....&#x &  5 0 | 2  8  0  0 |  6 4  0  0  0 0 | 1  4  0 0 0  0  0 0 | 6 *  * *  * | 1 0 1
x..x o..x o..x&#x &  2 8 | 1  0  8 12 |  0 0  4  8  0 6 | 0  0  4 2 0  0  0 1 | * 3  * *  * | 0 2 0
xoox .... ....&#x &  4 2 | 1  5  6  1 |  2 2  1  2  6 0 | 0  1  0 0 2  2  1 0 | * * 12 *  * | 0 0 2
xo.x ox.x ....&#x &  4 4 | 2  4  8  4 |  4 0  4  4  4 1 | 1  0  2 0 0  4  0 0 | * *  * 6  * | 0 1 1
xo.x .... oo.x&#x &  3 4 | 1  2  8  4 |  1 0  2  6  4 1 | 0  0  1 1 0  2  2 0 | * *  * * 12 | 0 1 1
--------------------+-----+------------+-----------------+---------------------+-------------+------
xoo. oxo. oox.&#x    6 0 | 3 12  0  0 | 12 8  0  0  0 0 | 3 12  0 0 0  0  0 0 | 6 0  0 0  0 | 1 * *
xo.x ox.x oo.x&#x &  4 8 | 2  4 16 12 |  4 0  8 16  8 6 | 1  0  8 4 0  8  4 1 | 0 2  0 2  4 | * 3 *
xoox oxox ....&#x &  5 4 | 2  8 12  4 |  6 4  4  8 12 1 | 1  4  2 1 4  8  4 0 | 1 0  4 1  2 | * * 6

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