As abstract polytope stappyp is isomorphic to peppyp, thereby replacing pentagrams by pentagons resp. replacing stappy by peppy and stip by pip.

Incidence matrix according to Dynkin symbol

xx ox5/2oo&#x   → height = sqrt((5+sqrt(5))/10) = 0.850651
(line || stip)

o. o.5/2o.    | 2  * | 1  5 0  0 | 5  5 0 0 | 5 1 0
.o .o5/2.o    | * 10 | 0  1 1  2 | 1  2 2 1 | 2 1 1
--------------+------+-----------+----------+------
x. ..   ..    | 2  0 | 1  * *  * | 5  0 0 0 | 5 0 0
oo oo5/2oo&#x | 1  1 | * 10 *  * | 1  2 0 0 | 2 1 0
.x ..   ..    | 0  2 | *  * 5  * | 1  0 2 0 | 2 0 1
.. .x   ..    | 0  2 | *  * * 10 | 0  1 1 1 | 1 1 1
--------------+------+-----------+----------+------
xx ..   ..&#x | 2  2 | 1  2 1  0 | 5  * * * | 2 0 0
.. ox   ..&#x | 1  2 | 0  2 0  1 | * 10 * * | 1 1 0
.x .x   ..    | 0  4 | 0  0 2  2 | *  * 5 * | 1 0 1
.. .x5/2.o    | 0  5 | 0  0 0  5 | *  * * 2 | 0 1 1
--------------+------+-----------+----------+------
xx ox   ..&#x ♦ 2  4 | 1  4 2  2 | 2  2 1 0 | 5 * *
.. ox5/2oo&#x ♦ 1  5 | 0  5 0  5 | 0  5 0 1 | * 2 *
.x .x5/2.o    ♦ 0 10 | 0  0 5 10 | 0  0 5 2 | * * 1

stappy || stappy   → height = 1

  1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0  top-tip
  * 5 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
  * * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1  bottom-tip
  * * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
  1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
  1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
  0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
  0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
  0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1
  0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
  1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
  1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0
  0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
  0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0
  0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1
  0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * *
♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 *
♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1

oxxo5/2oooo&#xr   → height(1,2) = height(3,4) = sqrt((5+sqrt(5))/10) = 0.850651
                    height(1,4) = height(2,3) = 1
( (pt || {5/2})  ||  (pt || {5/2}) )

o...5/2o...     | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0
.o..5/2.o..     | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
..o.5/2..o.     | * * 5 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1
...o5/2...o     | * * * 1 | 0 1 0 0 0 5 | 0 5 0 0 0 5 | 0 5 0 1
----------------+---------+-------------+-------------+--------
oo..5/2oo..&#x  | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o..o5/2o..o&#x  | 1 0 0 1 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
.x..   ....     | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
.oo.5/2.oo.&#x  | 0 1 1 0 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
..x.   ....     | 0 0 2 0 | * * * * 5 * | 0 0 0 1 1 1 | 0 1 1 1
..oo5/2..oo&#x  | 0 0 1 1 | * * * * * 5 | 0 1 0 0 0 2 | 0 2 0 1
----------------+---------+-------------+-------------+--------
ox..   ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
oooo5/2oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 5 * * * * | 0 2 0 0
.x..5/2.o..     | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
.xx.   ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 | * * * 5 * * | 0 1 1 0
..x.5/2..o.     | 0 0 5 0 | 0 0 0 0 5 0 | * * * * 1 * | 0 0 1 1
..xo   ....&#x  | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 5 | 0 1 0 1
----------------+---------+-------------+-------------+--------
ox..5/2oo..&#x  ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
oxxo   ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 5 * *
.xx.5/2.oo.&#x  ♦ 0 5 5 0 | 0 0 5 5 5 0 | 0 0 1 5 1 0 | * * 1 *
..xo5/2..oo&#x  ♦ 0 0 5 1 | 0 0 0 0 5 5 | 0 0 0 0 1 5 | * * * 1

o(xo)x5/2o(oo)o&#xt 
(pt || ({5/2} || pt) || para {5/2})

o(..).5/2o(..).     | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0
.(o.).5/2.(o.).     | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.(.o).5/2.(.o).     | * * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1
.(..)o5/2.(..)o     | * * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1
--------------------+---------+-------------+-------------+--------
o(o.).5/2o(o.).&#x  | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o(.o).5/2o(.o).&#x  | 1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
.(x.).   .(..).     | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
.(o.)o5/2.(o.)o&#x  | 0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
.(.o)o5/2.(.o)o&#x  | 0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1
.(..)x   .(..).     | 0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1
--------------------+---------+-------------+-------------+--------
o(x.).   .(..).&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
o(oo)o5/2o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0
.(x.).5/2.(o.).     | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
.(x.)x   .(..).&#x  | 0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0
.(.o)x   .(..).&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1
.(..)x5/2.(..)o     | 0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1
--------------------+---------+-------------+-------------+--------
o(x.).5/2o(o.).&#x  ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
o(xo)x   .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * *
.(x.)x5/2.(o.)o&#x  ♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 *
.(.o)x5/2.(.o)o&#x  ♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1