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 triangle-gyrobifastegium likewise is the bistratic adjoin of 2 (trig, tet)-duoprisms, thereby blending out the common triddipic base.

Incidence matrix according to Dynkin symbol

xxo3ooo oxx3ooo&#xt   → both heigths = sqrt(2/3) = 0.816497
(trig || pseudo triddip || perp trig)

o..3o.. o..3o..    | 3 * * | 2 3 0 0 0 0 | 1 6 3 0 0 0 0 0 0 | 3 6 1 0 0 0 0 0 | 3 2 0 0
.o.3.o. .o.3.o.    | * 9 * | 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
..o3..o ..o3..o    | * * 3 | 0 0 0 0 3 2 | 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 1 6 3 | 0 0 2 3
-------------------+-------+-------------+-------------------+-----------------+--------
x.. ... ... ...    | 2 0 0 | 3 * * * * * | 1 3 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 | 3 1 0 0
oo.3oo. oo.3oo.&#x | 1 1 0 | * 9 * * * * | 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 | * * 9 * * * | 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 | * * * 9 * * | 0 0 1 0 2 1 0 1 0 | 0 2 1 1 2 0 2 1 | 1 2 1 2
.oo3.oo .oo3.oo&#x | 0 1 1 | * * * * 9 * | 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 3 1 | 0 0 0 0 0 0 3 3 | 0 0 1 3
-------------------+-------+-------------+-------------------+-----------------+--------
x..3o.. ... ...    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 3 0 0 0 0 0 0 0 | 3 0 0 0
xx. ... ... ...&#x | 2 2 0 | 1 2 1 0 0 0 | * 9 * * * * * * * | 2 1 0 0 0 0 0 0 | 2 1 0 0
... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 9 * * * * * * | 0 2 1 0 0 0 0 0 | 1 2 0 0
.x.3.o. ... ...    | 0 3 0 | 0 0 3 0 0 0 | * * * 3 * * * * * | 1 0 0 2 0 1 0 0 | 2 0 2 0
.x. ... .x. ...    | 0 4 0 | 0 0 2 2 0 0 | * * * * 9 * * * * | 0 1 0 1 1 0 1 0 | 1 1 1 1
... ... .x.3.o.    | 0 3 0 | 0 0 0 3 0 0 | * * * * * 3 * * * | 0 0 1 0 2 0 0 1 | 0 2 0 2
.xo ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * 9 * * | 0 0 0 0 0 1 2 0 | 0 0 2 1
... ... .xx ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 9 * | 0 0 0 0 0 0 2 1 | 0 0 1 2
... ... ..x3..o    | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 0 0 0 0 0 0 3 | 0 0 0 3
-------------------+-------+-------------+-------------------+-----------------+--------
xx.3oo. ... ...&#x ♦ 3 3 0 | 3 3 3 0 0 0 | 1 3 0 1 0 0 0 0 0 | 3 * * * * * * * | 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 | * 9 * * * * * * | 1 1 0 0
... ... ox.3oo.&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 3 0 0 1 0 0 0 | * * 3 * * * * * | 0 2 0 0
.x.3.o. .x. ...    ♦ 0 6 0 | 0 0 6 3 0 0 | 0 0 0 2 3 0 0 0 0 | * * * 3 * * * * | 1 0 1 0
.x. ... .x.3.o.    ♦ 0 6 0 | 0 0 3 6 0 0 | 0 0 0 0 3 2 0 0 0 | * * * * 3 * * * | 0 1 0 1
.xo3.oo ... ...&#x ♦ 0 3 1 | 0 0 3 0 3 0 | 0 0 0 1 0 0 3 0 0 | * * * * * 3 * * | 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 | * * * * * * 9 * | 0 0 1 1
... ... .xx3.oo&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 1 0 3 1 | * * * * * * * 3 | 0 0 0 2
-------------------+-------+-------------+-------------------+-----------------+--------
xx.3oo. ox. ...&#x ♦ 3 6 0 | 3 6 6 3 0 0 | 1 6 3 2 3 0 0 0 0 | 2 3 0 1 0 0 0 0 | 3 * * *
xx. ... ox.3oo.&#x ♦ 2 6 0 | 1 6 3 6 0 0 | 0 3 6 0 3 2 0 0 0 | 0 3 2 0 1 0 0 0 | * 3 * *
.xo3.oo .xx ...&#x ♦ 0 6 2 | 0 0 6 3 6 1 | 0 0 0 2 3 0 6 3 0 | 0 0 0 1 0 2 3 0 | * * 3 *
.xo ... .xx3.oo&#x ♦ 0 6 3 | 0 0 3 6 6 3 | 0 0 0 0 3 2 3 6 1 | 0 0 0 0 1 0 3 2 | * * * 3

or
o..3o.. o..3o..    & | 6 * | 2  3  0 | 1  6  3 0 0 | 3  6 1 0 | 3 2
.o.3.o. .o.3.o.      | * 9 | 0  2  4 | 0  4  4 2 4 | 2  8 2 4 | 4 4
---------------------+-----+---------+-------------+----------+----
x.. ... ... ...    & | 2 0 | 6  *  * | 1  3  0 0 0 | 3  3 0 0 | 3 1
oo.3oo. oo.3oo.&#x & | 1 1 | * 18  * | 0  2  2 0 0 | 1  4 1 0 | 2 2
.x. ... ... ...    & | 0 2 | *  * 18 | 0  1  1 1 2 | 1  4 1 3 | 3 3
---------------------+-----+---------+-------------+----------+----
x..3o.. ... ...    & | 3 0 | 3  0  0 | 2  *  * * * | 3  0 0 0 | 3 0
xx. ... ... ...&#x & | 2 2 | 1  2  1 | * 18  * * * | 1  2 0 0 | 2 1
... ... ox. ...&#x & | 1 2 | 0  2  1 | *  * 18 * * | 0  2 1 0 | 1 2
.x.3.o. ... ...    & | 0 3 | 0  0  3 | *  *  * 6 * | 1  0 1 2 | 2 2
.x. ... .x. ...      | 0 4 | 0  0  4 | *  *  * * 9 | 0  2 0 2 | 2 2
---------------------+-----+---------+-------------+----------+----
xx.3oo. ... ...&#x & ♦ 3 3 | 3  3  3 | 1  3  0 1 0 | 6  * * * | 2 0
xx. ... ox. ...&#x & ♦ 2 4 | 1  4  4 | 0  2  2 0 1 | * 18 * * | 1 1
... ... ox.3oo.&#x & ♦ 1 3 | 0  3  3 | 0  0  3 1 0 | *  * 6 * | 0 2
.x.3.o. .x. ...    & ♦ 0 6 | 0  0  9 | 0  0  0 2 3 | *  * * 6 | 1 1
---------------------+-----+---------+-------------+----------+----
xx.3oo. ox. ...&#x & ♦ 3 6 | 3  6  9 | 1  6  3 2 3 | 2  3 0 1 | 6 *
xx. ... ox.3oo.&#x & ♦ 2 6 | 1  6  9 | 0  3  6 2 3 | 0  3 2 1 | * 6