Acronym squix
Name square hixene,
square atop fully orthogonal pentachoron
|,>,O device line prism pyramid pyramid pyramid pyramid pyramid = ||>>>>>
Circumradius 1/sqrt(2) = 0.707107
Confer
uniform relative:
zee  
general polytopal classes:
segmentoexa   hixene  

Incidence matrix according to Dynkin symbol

xo4oo ox3oo3oo3oo&#x   → height = 1/sqrt(10) = 0.316228
({4} || perp pen)

o.4o. o.3o.3o.3o.    | 4 * | 2  5  0 | 1 10 10  0 | 5 20 10 0 | 10 20  5 0 | 10 10 1 | 5 2
.o4.o .o3.o3.o3.o    | * 5  0  4  4 | 0  4 16  6 | 1 16 24 4 |  4 24 16 1 |  6 16 4 | 4 4
---------------------+-----+---------+------------+-----------+------------+---------+----
x. .. .. .. .. ..    | 2 0 | 4  *  * | 1  5  0  0 | 5 10  0 0 | 10 10  0 0 | 10  5 0 | 5 1
oo4oo oo3oo3oo3oo&#x | 1 1 | * 20  * | 0  2  4  0 | 1  8  6 0 |  4 12  4 0 |  6  8 1 | 4 2
.. .. .x .. .. ..    | 0 2 | *  * 10  0  0  4  3 | 0  4 12 3 |  1 12 12 1 |  3 12 4 | 3 4
---------------------+-----+---------+------------+-----------+------------+---------+----
x.4o. .. .. .. ..    | 4 0 | 4  0  0 | 1  *  *  *  5  0  0 0 | 10  0  0 0 | 10  0 0 | 5 0
xo .. .. .. .. ..&#x | 2 1 | 1  2  0 | * 20  *  * | 1  4  0 0 |  4  6  0 0 |  6  4 0 | 4 1
.. .. ox .. .. ..&#x | 1 2 | 0  2  1 | *  * 40  * | 0  2  3 0 |  1  6  3 0 |  3  6 1 | 3 2
.. .. .x3.o .. ..    | 0 3 | 0  0  3 | *  *  * 10  0  0  4 2 |  0  4  8 1 |  1  8 4 | 2 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo .. .. .. ..&#x  4 1 | 4  4  0 | 1  4  0  0 | 5  *  * *   4  0  0 0 |  6  0 0 | 4 0
xo .. ox .. .. ..&#x  2 2 | 1  4  1 | 0  2  2  0 | * 40  * * |  1  3  0 0 |  3  3 0 | 3 1
.. .. ox3oo .. ..&#x  1 3 | 0  3  3 | 0  0  3  1 | *  * 40 * |  0  2  2 0 |  1  4 1 | 2 2
.. .. .x3.o3.o ..     0 4 | 0  0  6 | 0  0  0  4 | *  *  * 5   0  0  4 1 |  0  4 4 | 1 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox .. .. ..&#x  4 2 | 4  8  1 | 1  8  4  0 | 2  4  0 0 | 10  *  * * |  3  0 0 | 3 0
xo .. ox3oo .. ..&#x  2 3 | 1  6  3 | 0  3  6  1 | 0  3  2 0 |  * 40  * * |  1  2 0 | 2 1
.. .. ox3oo3oo ..&#x  1 4 | 0  4  6 | 0  0  6  4 | 0  0  4 1 |  *  * 20 * |  0  2 1 | 1 2
.. .. .x3.o3.o3.o     0 5 | 0  0 10 | 0  0  0 10 | 0  0  0 5 |  *  *  * 1 |  0  0 4 | 0 4
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox3oo .. ..&#x  4 3 | 4 12  3 | 1 12 12  1 | 3 12  4 0 |  3  4  0 0 | 10  * * | 2 0
xo .. ox3oo3oo ..&#x  2 4 | 1  8  6 | 0  4 12  4 | 0  6  8 1 |  0  4  2 0 |  * 20 * | 1 1
.. .. ox3oo3oo3oo&#x  1 5 | 0  5 10 | 0  0 10 10 | 0  0 10 5 |  0  0  5 1 |  *  * 4 | 0 2
---------------------+-----+---------+------------+-----------+------------+---------+----
xo4oo ox3oo3oo ..&#x  4 4 | 4 16  6 | 1 16 24  4 | 4 24 16 1 |  6 16  4 0 |  4  4 0 | 5 *
xo .. ox3oo3oo3oo&#x  2 5 | 1 10 10 | 0  5 20 10 | 0 10 20 5 |  0 10 10 1 |  0  5 2 | * 4

oxx xoo3ooo3ooo3ooo&#x   → height(1,2) = height(1,3) = sqrt(7/20) = 0.591608
                           height(2,3) = 1

o.. o..3o..3o..3o..    | 5 * *   4  2  2 0 0 0 |  6 1  8  2 1  8 0 | 4  4 12 1  8  4 12 | 1  6  8  4 12  6  8 | 4 2  6  8 4 2 | 1 4 2 1
.o. .o.3.o.3.o.3.o.    | * 2 * |  0  5  0 1 1 0 |  0 5 10  5 0  0 1 | 0 10 10 5 10  0  0 | 0 10  5 10 10  0  0 | 5 1 10  5 0 0 | 1 5 1 0
..o ..o3..o3..o3..o    | * * 2 |  0  0  5 0 1 1 |  0 0  0  5 5 10 1 | 0  0  0 5 10 10 10 | 0  0  0 10 10 10  5 | 0 0 10  5 5 1 | 0 5 1 1
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
... x.. ... ... ...    | 2 0 0 | 10  *  * * * *   3 0  2  0 0  2 0 | 3  1  6 0  2  1  6 | 1  3  6  1  6  3  6 | 3 2  3  6 3 2 | 1 3 2 1
oo. oo.3oo.3oo.3oo.&#x | 1 1 0 |  * 10  * * * * |  0 1  4  1 0  0 0 | 0  4  6 1  4  0  0 | 0  6  4  4  6  0  0 | 4 1  6  4 0 0 | 1 4 1 0
o.o o.o3o.o3o.o3o.o&#x | 1 0 1 |  *  * 10 * * * |  0 0  0  1 1  4 0 | 0  0  0 1  4  4  6 | 0  0  0  4  6  6  4 | 0 0  6  4 4 1 | 0 4 1 1
.x. ... ... ... ...    | 0 2 0 |  *  *  * 1 * * |  0 5  0  0 0  0 1 | 0 10  0 5  0  0  0 | 0 10  0 10  0  0  0 | 5 0 10  0 0 0 | 1 5 0 0
.oo .oo3.oo3.oo3.oo&#x | 0 1 1 |  *  *  * * 2 * |  0 0  0  5 0  0 1 | 0  0  0 5 10  0  0 | 0  0  0 10 10  0  0 | 0 0 10  5 0 0 | 0 5 1 0
..x ... ... ... ...    | 0 0 2 |  *  *  * * * 1 |  0 0  0  0 5  0 1 | 0  0  0 5  0 10  0 | 0  0  0 10  0 10  0 | 0 0 10  0 5 0 | 0 5 0 1
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
... x..3o.. ... ...    | 3 0 0 |  3  0  0 0 0 0 | 10 *  *  * *  * *  2  0  2 0  0  0  2 | 1  1  4  0  2  1  4 | 2 2  1  4 2 2 | 1 2 2 1
ox. ... ... ... ...&#x | 1 2 0 |  0  2  0 1 0 0 |  * 5  *  * *  * * | 0  4  0 1  0  0  0 | 0  6  0  4  0  0  0 | 4 0  6  0 0 0 | 1 4 0 0
... xo. ... ... ...&#x | 2 1 0 |  1  2  0 0 0 0 |  * * 20  * *  * * | 0  1  3 0  1  0  0 | 0  3  3  1  3  0  0 | 3 1  3  3 0 0 | 1 3 1 0
ooo ooo3ooo3ooo3ooo&#x | 1 1 1 |  0  1  1 0 1 0 |  * *  * 10 *  * * | 0  0  0 1  4  0  0 | 0  0  0  4  6  0  0 | 0 0  6  4 0 0 | 0 4 1 0
o.x ... ... ... ...&#x | 1 0 2 |  0  0  2 0 0 1 |  * *  *  * 5  * * | 0  0  0 1  0  4  0 | 0  0  0  4  0  6  0 | 0 0  6  0 4 0 | 0 4 0 1
... x.o ... ... ...&#x | 2 0 1 |  1  0  2 0 0 0 |  * *  *  * * 20 * | 0  0  0 0  1  1  3 | 0  0  0  1  3  3  3 | 0 0  3  3 3 1 | 0 3 1 1
.xx ... ... ... ...&#x | 0 2 2 |  0  0  0 1 2 1 |  * *  *  * *  * 1  0  0  0 5  0  0  0 | 0  0  0 10  0  0  0 | 0 0 10  0 0 0 | 0 5 0 0
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
... x..3o..3o.. ...     4 0 0 |  6  0  0 0 0 0 |  4 0  0  0 0  0 0 | 5  *  * *  *  *  *  1  0  2  0  0  0  2 | 1 2  0  2 1 2 | 1 1 2 1
ox. xo. ... ... ...&#x  2 2 0 |  1  4  0 1 0 0 |  0 2  2  0 0  0 0 | * 10  * *  *  *  * | 0  3  0  1  0  0  0 | 3 0  3  0 0 0 | 1 3 0 0
... xo.3oo. ... ...&#x  3 1 0 |  3  3  0 0 0 0 |  1 0  3  0 0  0 0 | *  * 20 *  *  *  * | 0  1  2  0  1  0  0 | 2 1  1  2 0 0 | 1 2 1 0
oxx ... ... ... ...&#x  1 2 2 |  0  2  2 1 2 1 |  0 1  0  2 1  0 1 | *  *  * 5  *  *  *  0  0  0  4  0  0  0 | 0 0  6  0 0 0 | 0 4 0 0
... xoo ... ... ...&#x  2 1 1 |  1  2  2 0 1 0 |  0 0  1  2 0  1 0 | *  *  * * 20  *  * | 0  0  0  1  3  0  0 | 0 0  3  3 0 0 | 0 3 1 0
o.x x.o ... ... ...&#x  2 0 2 |  1  0  4 0 0 1 |  0 0  0  0 2  2 0 | *  *  * *  * 10  * | 0  0  0  1  0  3  0 | 0 0  3  0 3 0 | 0 3 0 1
... x.o3o.o ... ...&#x  3 0 1 |  3  0  3 0 0 0 |  1 0  0  0 0  3 0 | *  *  * *  *  * 20 | 0  0  0  0  1  1  2 | 0 0  1  2 2 1 | 0 2 1 1
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
... x..3o..3o..3o..     5 0 0 | 10  0  0 0 0 0 | 10 0  0  0 0  0 0 | 5  0  0 0  0  0  0 | 1  *  *  *  *  *  * | 0 2  0  0 0 2 | 1 0 2 1
ox. xo.3oo. ... ...&#x  3 2 0 |  3  6  0 1 0 0 |  1 3  6  0 0  0 0 | 0  3  2 0  0  0  0 | * 10  *  *  *  *  * | 2 0  1  0 0 0 | 1 2 0 0
... xo.3oo.3oo. ...&#x  4 1 0 |  6  4  0 0 0 0 |  4 0  6  0 0  0 0 | 1  0  4 0  0  0  0 | *  * 10  *  *  *  * | 1 1  0  1 0 0 | 1 1 1 0
oxx xoo ... ... ...&#x  2 2 2 |  1  4  4 1 2 1 |  0 2  2  4 2  2 1 | 0  1  0 2  2  1  0 | *  *  * 10  *  *  * | 0 0  3  0 0 0 | 0 3 0 0
... xoo3ooo ... ...&#x  3 1 1 |  3  3  3 0 1 0 |  1 0  3  3 0  3 0 | 0  0  1 0  3  0  1 | *  *  *  * 20  *  * | 0 0  1  2 0 0 | 0 2 1 0
o.x x.o3o.o ... ...&#x  3 0 2 |  3  0  6 0 0 1 |  1 0  0  0 3  6 0 | 0  0  0 0  0  3  2 | *  *  *  *  * 10  * | 0 0  1  0 2 0 | 0 2 0 1
... x.o3o.o3o.o ...&#x  4 0 1 |  6  0  4 0 0 0 |  4 0  0  0 0  6 0 | 1  0  0 0  0  0  4 | *  *  *  *  *  * 10 | 0 0  0  1 1 1 | 0 1 1 1
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
ox. xo.3oo.3oo. ...&#x  4 2 0 |  6  8  0 1 0 0 |  4 4 12  0 0  0 0 | 1  6  8 0  0  0  0 | 0  4  2  0  0  0  0 | 5 *  *  * * * | 1 1 0 0
... xo.3oo.3oo.3oo.&#x  5 1 0 | 10  5  0 0 0 0 | 10 0 10  0 0  0 0 | 5  0 10 0  0  0  0 | 1  0  5  0  0  0  0 | * 2  *  * * * | 1 0 1 0
oxx xoo3ooo ... ...&#x  3 2 2 |  3  6  6 1 2 1 |  1 3  6  6 3  6 1 | 0  3  2 3  6  3  2 | 0  1  0  3  2  1  0 | * * 10  * * * | 0 2 0 0
... xoo3ooo3ooo ...&#x  4 1 1 |  6  4  4 0 1 0 |  4 0  6  4 0  6 0 | 1  0  4 0  6  0  4 | 0  0  1  0  4  0  1 | * *  * 10 * * | 0 1 1 0
o.x x.o3o.o3o.o ...&#x  4 0 2 |  6  0  8 0 0 1 |  4 0  0  0 4 12 0 | 1  0  0 0  0  6  8 | 0  0  0  0  0  4  2 | * *  *  * 5 * | 0 1 0 1
... x.o3o.o3o.o3o.o&#x  5 0 1 | 10  0  5 0 0 0 | 10 0  0  0 0 10 0 | 5  0  0 0  0  0 10 | 1  0  0  0  0  0  5 | * *  *  * * 2 | 0 0 1 1
-----------------------+-------+----------------+-------------------+--------------------+---------------------+---------------+--------
ox. xo.3oo.3oo.3oo.&#x  5 2 0 | 10 10  0 1 0 0 | 10 5 20  0 0  0 0 | 5 10 20 0  0  0  0 | 1 10 10  0  0  0  0 | 5 2  0  0 0 0 | 1 * * *
oxx xoo3ooo3ooo ...&#x  4 2 2 |  6  8  8 1 2 1 |  4 4 12  8 4 12 1 | 1  6  8 4 12  6  8 | 0  4  2  6  8  4  2 | 1 0  4  2 1 0 | * 5 * *
... xoo3ooo3ooo3ooo&#x  5 1 1 | 10  5  5 0 1 0 | 10 0 10  5 0 10 0 | 5  0 10 0 10  0 10 | 1  0  5  0 10  0  5 | 0 1  0  5 0 1 | * * 2 *
o.x x.o3o.o3o.o3o.o&#x  5 0 2 | 10  0 10 0 0 1 | 10 0  0  0 5 20 0 | 5  0  0 0  0 10 20 | 1  0  0  0  0 10 10 | 0 0  0  0 5 2 | * * * 1

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