Just as the 3D gyrobifastegium just was the bistratic lace tower, obtained as external blend of 2 square-adjoined trips (then in the sense of line || pseudo square || perp line), this 5D square-gyrobifastegium likewise is the bistratic adjoin of 2 (square, squippy)-duoprisms, thereby blending out the common tessic base.

Incidence matrix according to Dynkin symbol

xxo4ooo oxx4ooo&#xt   → both heigths = 1/sqrt(2) = 0.707107
(square || pseudo tes || perp square)

o..4o.. o..4o..    | 4  * * | 2  4  0  0  0 0 | 1  8  4 0  0 0  0  0 0 | 4  8 1 0 0 0  0 0 | 4 2 0 0
.o.4.o. .o.4.o.    | * 16 * | 0  1  2  2  1 0 | 0  2  2 1  4 1  2  2 0 | 1  4 1 2 2 1  4 1 | 2 2 2 2
..o4..o ..o4..o    | *  * 4 | 0  0  0  0  4 2 | 0  0  0 0  0 0  4  8 1 | 0  0 0 0 0 1  8 4 | 0 0 2 4
-------------------+--------+-----------------+------------------------+-------------------+--------
x.. ... ... ...    | 2  0 0 | 4  *  *  *  * * | 1  4  0 0  0 0  0  0 0 | 4  4 0 0 0 0  0 0 | 4 1 0 0
oo.4oo. oo.4oo.&#x | 1  1 0 | * 16  *  *  * * | 0  2  2 0  0 0  0  0 0 | 1  4 1 0 0 0  0 0 | 2 2 0 0
.x. ... ... ...    | 0  2 0 | *  * 16  *  * * | 0  1  0 1  2 0  1  0 0 | 1  2 0 2 1 1  2 0 | 2 1 2 1
... ... .x. ...    | 0  2 0 | *  *  * 16  * * | 0  0  1 0  2 1  0  1 0 | 0  2 1 1 2 0  2 1 | 1 2 1 2
.oo4.oo .oo4.oo&#x | 0  1 1 | *  *  *  * 16 * | 0  0  0 0  0 0  2  2 0 | 0  0 0 0 0 1  4 1 | 0 0 2 2
... ... ..x ...    | 0  0 2 | *  *  *  *  * 4 | 0  0  0 0  0 0  0  4 1 | 0  0 0 0 0 0  4 4 | 0 0 1 4
-------------------+--------+-----------------+------------------------+-------------------+--------
x..4o.. ... ...    | 4  0 0 | 4  0  0  0  0 0 | 1  *  * *  * *  *  * * | 4  0 0 0 0 0  0 0 | 4 0 0 0
xx. ... ... ...&#x | 2  2 0 | 1  2  1  0  0 0 | * 16  * *  * *  *  * * | 2  1 0 0 0 0  0 0 | 2 1 0 0
... ... ox. ...&#x | 1  2 0 | 0  2  0  1  0 0 | *  * 16 *  * *  *  * * | 0  2 1 0 0 0  0 0 | 1 2 0 0
.x.4.o. ... ...    | 0  4 0 | 0  0  4  0  0 0 | *  *  * 4  * *  *  * * | 1  0 0 2 0 1  0 0 | 2 0 2 0
.x. ... .x. ...    | 0  4 0 | 0  0  2  2  0 0 | *  *  * * 16 *  *  * * | 0  1 0 1 1 0  1 0 | 1 1 1 1
... ... .x.4.o.    | 0  4 0 | 0  0  0  4  0 0 | *  *  * *  * 4  *  * * | 0  0 1 0 2 0  0 1 | 0 2 0 2
.xo ... ... ...&#x | 0  2 1 | 0  0  1  0  2 0 | *  *  * *  * * 16  * * | 0  0 0 0 0 1  2 0 | 0 0 2 1
... ... .xx ...&#x | 0  2 2 | 0  0  0  1  2 1 | *  *  * *  * *  * 16 * | 0  0 0 0 0 0  2 1 | 0 0 1 2
... ... ..x4..o    | 0  0 4 | 0  0  0  0  0 4 | *  *  * *  * *  *  * 1 | 0  0 0 0 0 0  0 4 | 0 0 0 4
-------------------+--------+-----------------+------------------------+-------------------+--------
xx.4oo. ... ...&#x ♦ 4  4 0 | 4  4  4  0  0 0 | 1  4  0 1  0 0  0  0 0 | 4  * * * * *  * * | 2 0 0 0
xx. ... ox. ...&#x ♦ 2  4 0 | 1  4  2  2  0 0 | 0  2  2 0  1 0  0  0 0 | * 16 * * * *  * * | 1 1 0 0
... ... ox.4oo.&#x ♦ 1  4 0 | 0  4  0  4  0 0 | 0  0  4 0  0 1  0  0 0 | *  * 4 * * *  * * | 0 2 0 0
.x.4.o. .x. ...    ♦ 0  8 0 | 0  0  8  4  0 0 | 0  0  0 2  4 0  0  0 0 | *  * * 4 * *  * * | 1 0 1 0
.x. ... .x.4.o.    ♦ 0  8 0 | 0  0  4  8  0 0 | 0  0  0 0  4 2  0  0 0 | *  * * * 4 *  * * | 0 1 0 1
.xo4.oo ... ...&#x ♦ 0  4 1 | 0  0  4  0  4 0 | 0  0  0 1  0 0  4  0 0 | *  * * * * 4  * * | 0 0 2 0
.xo ... .xx ...&#x ♦ 0  4 2 | 0  0  2  2  4 1 | 0  0  0 0  1 0  2  2 0 | *  * * * * * 16 * | 0 0 1 1
... ... .xx4.oo&#x ♦ 0  4 4 | 0  0  0  4  4 4 | 0  0  0 0  0 1  0  4 1 | *  * * * * *  * 4 | 0 0 0 2
-------------------+--------+-----------------+------------------------+-------------------+--------
xx.4oo. ox. ...&#x ♦ 4  8 0 | 4  8  8  4  0 0 | 1  8  4 2  4 0  0  0 0 | 2  4 0 1 0 0  0 0 | 4 * * *
xx. ... ox.4oo.&#x ♦ 2  8 0 | 1  8  4  8  0 0 | 0  4  8 0  4 2  0  0 0 | 0  4 2 0 1 0  0 0 | * 4 * *
.xo4.oo .xx ...&#x ♦ 0  8 2 | 0  0  8  4  8 1 | 0  0  0 2  4 0  8  4 0 | 0  0 0 1 0 2  4 0 | * * 4 *
.xo ... .xx4.oo&#x ♦ 0  8 4 | 0  0  4  8  8 4 | 0  0  0 0  4 2  4  8 1 | 0  0 0 0 1 0  4 2 | * * * 4

or
o..4o.. o..4o..    & | 8  * | 2  4  0 | 1  8  4 0  0 | 4  8 1 0 | 4 2
.o.4.o. .o.4.o.      | * 16 | 0  2  4 | 0  4  4 2  4 | 2  8 2 4 | 4 4
---------------------+------+---------+--------------+----------+----
x.. ... ... ...    & | 2  0 | 8  *  * | 1  4  0 0  0 | 4  4 0 0 | 4 1
oo.4oo. oo.4oo.&#x & | 1  1 | * 32  * | 0  2  2 0  0 | 1  4 1 0 | 2 2
.x. ... ... ...    & | 0  2 | *  * 32 | 0  1  1 1  2 | 1  4 1 3 | 3 3
---------------------+------+---------+--------------+----------+----
x..4o.. ... ...    & | 4  0 | 4  0  0 | 2  *  * *  * | 4  0 0 0 | 4 0
xx. ... ... ...&#x & | 2  2 | 1  2  1 | * 32  * *  * | 1  2 0 0 | 2 1
... ... ox. ...&#x & | 1  2 | 0  2  1 | *  * 32 *  * | 0  2 1 0 | 1 2
.x.4.o. ... ...    & | 0  4 | 0  0  4 | *  *  * 8  * | 1  0 1 2 | 2 2
.x. ... .x. ...      | 0  4 | 0  0  4 | *  *  * * 16 | 0  2 0 2 | 2 2
---------------------+------+---------+--------------+----------+----
xx.4oo. ... ...&#x & ♦ 4  4 | 4  4  4 | 1  4  0 1  0 | 8  * * * | 2 0
xx. ... ox. ...&#x & ♦ 2  4 | 1  4  4 | 0  2  2 0  1 | * 32 * * | 1 1
... ... ox.4oo.&#x & ♦ 1  4 | 0  4  4 | 0  0  4 1  0 | *  * 8 * | 0 2
.x.4.o. .x. ...    & ♦ 0  8 | 0  0 12 | 0  0  0 2  4 | *  * * 8 | 1 1
---------------------+------+---------+--------------+----------+----
xx.4oo. ox. ...&#x & ♦ 4  8 | 4  8 12 | 1  8  4 2  4 | 2  4 0 1 | 8 *
xx. ... ox.4oo.&#x & ♦ 2  8 | 1  8 12 | 0  4  8 2  4 | 0  4 2 1 | * 8