As abstract polytope stoct is isomorphic to poct, thereby replacing pentagrams by pentagons, resp. stip by pip, resp. tistadip by trapedip.

Incidence matrix according to Dynkin symbol

x5/2o x3o4o

.   . . . . | 30 |  2  4 | 1  8  4 |  4  8 1 | 4 2
------------+----+-------+---------+---------+----
x   . . . . |  2 | 30  * | 1  4  0 |  4  4 0 | 4 1
.   . x . . |  2 |  * 60 | 0  2  2 |  1  4 1 | 2 2
------------+----+-------+---------+---------+----
x5/2o . . . |  5 |  5  0 | 6  *  * |  4  0 0 | 4 0
x   . x . . |  4 |  2  2 | * 60  * |  1  2 0 | 2 1
.   . x3o . |  3 |  0  3 | *  * 40 |  0  2 1 | 1 2
------------+----+-------+---------+---------+----
x5/2o x . . ♦ 10 | 10  5 | 2  5  0 | 12  * * | 2 0
x   . x3o . ♦  6 |  3  6 | 0  3  2 |  * 40 * | 1 1
.   . x3o4o ♦  6 |  0 12 | 0  0  8 |  *  * 5 | 0 2
------------+----+-------+---------+---------+----
x5/2o x3o . ♦ 15 | 15 15 | 3 15  5 |  3  5 0 | 8 *
x   . x3o4o ♦ 12 |  6 24 | 0 12 16 |  0  8 2 | * 5

x5/2o o3x3o

.   . . . . | 30 |  2  4 | 1  8  2  2 |  4  4  4 1 | 2 2 2
------------+----+-------+------------+------------+------
x   . . . . |  2 | 30  * | 1  4  0  0 |  4  2  2 0 | 2 2 1
.   . . x . |  2 |  * 60 | 0  2  1  1 |  1  2  2 1 | 1 1 2
------------+----+-------+------------+------------+------
x5/2o . . . |  5 |  5  0 | 6  *  *  * |  4  0  0 0 | 2 2 0
x   . . x . |  4 |  2  2 | * 60  *  * |  1  1  1 0 | 1 1 1
.   . o3x . |  3 |  0  3 | *  * 20  * |  0  2  0 1 | 1 0 2
.   . . x3o |  3 |  0  3 | *  *  * 20 |  0  0  2 1 | 0 1 2
------------+----+-------+------------+------------+------
x5/2o . x . ♦ 10 | 10  5 | 2  5  0  0 | 12  *  * * | 1 1 0
x   . o3x . ♦  6 |  3  6 | 0  3  2  0 |  * 20  * * | 1 0 1
x   . . x3o ♦  6 |  3  6 | 0  3  0  2 |  *  * 20 * | 0 1 1
.   . o3x3o ♦  6 |  0 12 | 0  0  4  4 |  *  *  * 5 | 0 0 2
------------+----+-------+------------+------------+------
x5/2o o3x . ♦ 15 | 15 15 | 3 15  5  0 |  3  5  0 0 | 4 * *
x5/2o . x3o ♦ 15 | 15 15 | 3 15  0  5 |  3  0  5 0 | * 4 *
x   . o3x3o ♦ 12 |  6 24 | 0 12  8  8 |  0  4  4 2 | * * 5

xo3ox xx5/2oo&#x     → height = sqrt(2/3) = 0.816497
(tistadip || {3}-gyro tistadip)

o.3o. o.5/2o.    | 15  * |  2  2  2  0  0 | 1  4 1  2  1  4 0  0 0 | 2 2 1  4  2 2 0 0 | 1 2 2 1 0
.o3.o .o5/2.o    |  * 15 |  0  0  2  2  2 | 0  0 0  1  2  4 1  4 1 | 0 0 1  2  4 2 2 2 | 0 2 1 2 1
-----------------+-------+----------------+------------------------+-------------------+----------
x. .. ..   ..    |  2  0 | 15  *  *  *  * | 1  2 0  1  0  0 0  0 0 | 2 1 1  2  0 0 0 0 | 1 2 1 0 0
.. .. x.   ..    |  2  0 |  * 15  *  *  * | 0  2 1  0  0  2 0  0 0 | 1 2 0  2  1 2 0 0 | 1 2 2 1 0
oo3oo oo5/2oo&#x |  1  1 |  *  * 30  *  * | 0  0 0  1  1  2 0  0 0 | 0 0 1  2  2 1 0 0 | 0 1 1 1 0
.. .x ..   ..    |  0  2 |  *  *  * 15  * | 0  0 0  0  1  0 1  2 0 | 0 0 1  0  2 0 2 1 | 0 2 0 1 1
.. .. .x   ..    |  0  2 |  *  *  *  * 15 | 0  0 0  0  0  2 0  2 1 | 0 0 0  1  2 2 1 2 | 0 2 1 2 1
-----------------+-------+----------------+------------------------+-------------------+----------
x.3o. ..   ..    |  3  0 |  3  0  0  0  0 | 5  * *  *  *  * *  * * | 2 0 1  0  0 0 0 0 | 1 2 0 0 0
x. .. x.   ..    |  4  0 |  2  2  0  0  0 | * 15 *  *  *  * *  * * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.5/2o.    |  5  0 |  0  5  0  0  0 | *  * 3  *  *  * *  * * | 0 2 0  0  0 2 0 0 | 1 0 2 1 0
xo .. ..   ..&#x |  2  1 |  1  0  2  0  0 | *  * * 15  *  * *  * * | 0 0 1  2  0 0 0 0 | 0 2 1 0 0
.. ox ..   ..&#x |  1  2 |  0  0  2  1  0 | *  * *  * 15  * *  * * | 0 0 1  0  2 0 0 0 | 0 2 0 1 0
.. .. xx   ..&#x |  2  2 |  0  1  2  0  1 | *  * *  *  * 30 *  * * | 0 0 0  1  1 1 0 0 | 0 1 1 1 0
.o3.x ..   ..    |  0  3 |  0  0  0  3  0 | *  * *  *  *  * 5  * * | 0 0 1  0  0 0 2 0 | 0 2 0 0 1
.. .x .x   ..    |  0  4 |  0  0  0  2  2 | *  * *  *  *  * * 15 * | 0 0 0  0  1 0 1 1 | 0 1 0 1 1
.. .. .x5/2.o    |  0  5 |  0  0  0  0  5 | *  * *  *  *  * *  * 3 | 0 0 0  0  0 2 0 2 | 0 0 1 2 1
-----------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.   ..    ♦  6  0 |  6  3  0  0  0 | 2  3 0  0  0  0 0  0 0 | 5 * *  *  * * * * | 1 1 0 0 0
x. .. x.5/2o.    ♦ 10  0 |  5 10  0  0  0 | 0  5 2  0  0  0 0  0 0 | * 3 *  *  * * * * | 1 0 1 0 0
xo3ox ..   ..&#x ♦  3  3 |  3  0  6  3  0 | 1  0 0  3  3  0 1  0 0 | * * 5  *  * * * * | 0 2 0 0 0
xo .. xx   ..&#x ♦  4  2 |  2  2  4  0  1 | 0  1 0  2  0  2 0  0 0 | * * * 15  * * * * | 0 1 1 0 0
.. ox xx   ..&#x ♦  2  4 |  0  1  4  2  2 | 0  0 0  0  2  2 0  1 0 | * * *  * 15 * * * | 0 1 0 1 0
.. .. xx5/2oo&#x ♦  5  5 |  0  5  5  0  5 | 0  0 1  0  0  5 0  0 1 | * * *  *  * 6 * * | 0 0 1 1 0
.o3.x .x   ..    ♦  0  6 |  0  0  0  6  3 | 0  0 0  0  0  0 2  3 0 | * * *  *  * * 5 * | 0 1 0 0 1
.. .x .x5/2.o    ♦  0 10 |  0  0  0  5 10 | 0  0 0  0  0  0 0  5 2 | * * *  *  * * * 3 | 0 0 0 1 1
-----------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.5/2o.    ♦ 15  0 | 15 15  0  0  0 | 5 15 3  0  0  0 0  0 0 | 5 3 0  0  0 0 0 0 | 1 * * * *
xo3ox xx   ..&#x ♦  6  6 |  6  6  6  6  6 | 2  3 0  6  6  6 2  3 0 | 1 0 2  3  3 0 1 0 | * 5 * * *
xo .. xx5/2oo&#x ♦ 10  5 |  5 10 10  0  5 | 0  5 2  5  0 10 0  0 1 | 0 1 0  5  0 2 0 0 | * * 3 * *
.. ox xx5/2oo&#x ♦  5 10 |  0  5 10  5 10 | 0  0 1  0  5 10 0  5 2 | 0 0 0  0  5 2 0 1 | * * * 3 *
.o3.x .x5/2.o    ♦  0 15 |  0  0  0 15 15 | 0  0 0  0  0  0 5 15 3 | 0 0 0  0  0 0 5 3 | * * * * 1